Linearity

Problem 7001

For each value of $y$ , check if it satisfies $3y + 4 \geq -14$ . Values: -9, 2, -3, -6.

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Problem 7002

Solve the compound inequality: $5 < 3x + 2 < 17$ and graph the solution on a number line.

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Problem 7003

Check if each $x$ satisfies the inequality $69 \leq 7x + 6$ . Is it a solution? (Yes/No) for $x = 10, -6, 9, 2$ .

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Problem 7004

Translate to an inequality: $2y - 4 \geq -29$ .

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Problem 7005

Find $k$ in $y=kx$ and complete the values for $y$ when $x$ is 1, 4, 6, 10, 11, and 15.

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Problem 7006

Solve the compound inequality: $3 \leq \frac{1}{4} x + 4 < 5$ .

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Problem 7007

Choose the correct solution for each inequality and provide the answer if applicable. (a) $5(3-u)+5u>17$ (b) $-2(v+6)+28 \leq 4(3-v)$

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Problem 7008

Solve the system by the elimination method. $\begin{array}{l} 6 x=3 y-2 \\ 5 x+1=7 y \end{array}$

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Problem 7009

$7 / 32$ A line is perpendicular to $\mathrm{y}=2 \mathrm{x}-7$ . What is the slope of this line? $-1 / 2$ $-2$ 2 $1 / 2$

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Problem 7010

8. Which of the following equations is perpendicular to the line $2 x+3 y=6$ ? a. $y=-\frac{1}{2} x+4$ c. $y=-\frac{3}{2} x+1$ b. $y=\frac{3}{2} x-1$ d. $y=2 x+3$

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Problem 7011

Give the slope between the points $(-4,-2) \quad(5,-13)$ OK

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Problem 7012

What is the value of $y$ ? $\begin{array}{l} 9 y=27 \\ \frac{9 y}{9}=\frac{27}{9} \end{array}$ $y=$

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Problem 7013

- Higher Level
Ilowing simultaneous equations for $x, y, w \in \mathbb{Z}$ : $\begin{aligned} x+2 y & =143 \\ y+3 w & =-74 \\ 4 x+5 w & =4 \end{aligned}$

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Problem 7014

The graph of linear function $f$ passes through the point $(1,-9)$ and has a slope of -3 .
What is the zero of $f$ ?
F 2 G 4 H -6 J -2

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Problem 7015

7 AM Sat Dec 14 < <> S Savvas EasyBridge AA MATHEMATICS, GR 8 (FULL)-1(A)-24-25 3.4 MathXL (5 problems) savvasrealize.com S Savvas Realize DUE Savvas Realize Nov 18-11:59 pm Late A car moving at a constant speed passed a timing device at t=0. After 7 seconds, the car has traveled 588 ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device. The linear function rule is d = ☐ -

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Problem 7016

57. $-5>p-\frac{1}{5}$

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Problem 7017

Is $y-4=3(x+1)$ an equation of a line through $(-2,1)$ ? Explain.

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Problem 7018

13.
Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

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Problem 7019

11. Miguel's paycheck is $\$ 871.25$ . The paycheck includes 36.5 hours of work and a $\$ 50$ bonus. How much does Miguel earn for each hour of work, not including the bonus?

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Problem 7020

B) Graph the inequality. $3 x-2 y<18$

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Problem 7021

Solve the compound inequality: $4y + 3 \geq 19$ and $2y + 2 \geq -4$ . Provide the solution in interval notation.

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Problem 7022

Solve the inequality: $-4x \geq 8$ or $2x - 2 > 8$ . Provide the solution in interval notation or as $\varnothing$ .

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Problem 7023

Solve and justify the first step for: 1. $x + 4 + 3x = 72$ ; 2. $x + 3 + x - 8 + x = 55$ .

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Problem 7024

Solve $x + 3 + x - 8 + x = 55$ . What property justifies your first step?

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Problem 7025

Solve $x+3+x-8+x=55$ and $\frac{1}{2} x+10=\frac{1}{4} x+54$ . Explain your first step and its justification.

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Problem 7026

Solve $\frac{1}{2} x+10=\frac{1}{4} x+54$ . Explain your first step and the property used.

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Problem 7027

Solve $\frac{x+x+2}{4}=189.5$ . Explain the property used for your first step and your reasoning.

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Problem 7028

Solve the equation $\frac{1}{4} x + 18 = x$ and explain the property used for your first step.

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Problem 7029

Thu is 5 years older than Tuan. Their ages add up to 51. Find their ages: $T + (T + 5) = 51$ .

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Problem 7030

Tomás thinks of a number. If he triples it and subtracts 13, he gets 305. What is the number? Solve: $3x - 13 = 305$ .

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Problem 7031

Find two consecutive numbers whose sum is 123. What are the numbers?

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Problem 7032

Find two consecutive even numbers that add up to 246.

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Problem 7033

Find two consecutive even numbers that add up to 246. What are the numbers?

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Problem 7034

Alysha solved $2 x-3-8 x=14+2 x-1$ . Find her mistake and solve the equation correctly. What is $x$ ?

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Problem 7035

Joe's age is 3 times Aaron's. Aaron is 6 years older than Christina. Their ages sum to 149. Find Christina's, Joe's, and Aaron's ages.

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Problem 7036

Solve for $y$ in the equation: $-5=9+y$ .

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Problem 7037

Solve for $n$ in the equation $\frac{n+2}{4}=1$ .

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Problem 7038

Luke swims at 3 m/s. What is the slope of the line on a graph with time on the $x$ -axis and distance on the $y$ -axis? Distance in 45 seconds is (45, ).

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Problem 7039

Evaluate $-\frac{7}{3} x + 10$ when $x = 6$ .

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Problem 7040

Calculate the slope between the points (18,-12) and (-11,17). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

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Problem 7041

Find the slope-intercept form of the line passing through $(-1,1)$ with a slope of $0$ .

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Problem 7042

Find the slope-intercept form of the line that passes through the points $(2,3)$ and $(4,2)$ .

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Problem 7043

Write an inequality for: The product of $2x$ and $16$ is at most $9$ .

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Problem 7044

$\frac{5 x-3}{2}=6$

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Problem 7045

Systems of Linear Equations: Tutorial 13 of 26 ? Question Plane $A$ is descending toward the local airport at a rate of 2,500 feet/minute. It is currently at an altitude of 12,000 feet. Plane $B$ is ascending from the same airport at a rate of 4,000 feet/minute. It is currently at an altitude of 1,000 feet. This system of equations models this real-world situation, where $x$ represents the time in minutes and $y$ represents the altitude in thousands of feet: $\begin{array}{l} y=12-2.5 x \\ y=1+4 x \end{array}$
Graph the lines of the two equations, and mark the point of intersection for the two lines. In approximately how many minutes will the two planes be at the same altitude? At what altitude will they be?

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Problem 7046

Aufgaben zum Einsetzungsverfahren 1) Lose wie in Beispiel 1: a) $\left\lvert\, \begin{array}{l}4 x+2 y=8 \\ y=8 x-1\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}2 x+y=6 \\ y=-4 x\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}6 x+y=-4 \\ y=-3 x+2\end{array}\right.$ 2) Lóse wie in Beispiel 2: a) $\left\lvert\, \begin{array}{l}x+y=11 \\ x=-3\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}x-5 y=-16 \\ -5 x+20 y=40\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}2 x+3 y=-30 \\ x=-2 y-30\end{array}\right.$ 3) Lơse wie in Beispiel 3: a) $\left\lvert\, \begin{array}{l}4 x+7 y=-8 \\ 4 x+3 y=8\end{array}\right.$ b) $\left\lvert\, \begin{array}{l}3 x+8 y=9 \\ 5 x-8 y=15\end{array}\right.$ c) $\left\lvert\, \begin{array}{l}7 x+19 y=-3 \\ 12 x+19 y=22\end{array}\right.$ (mache jeweils die Probe und überprüfe somit dein Ergebnis!)

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Problem 7047

Question 2: solve the system of equations by graphical method: $\begin{array}{l} \mathrm{x}+2 \mathrm{y}=4 \\ \mathrm{y}=\frac{-1}{2} x+2 \end{array}$

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Problem 7048

Copy and complete the table below for the graph of $y=2 x+1$ . What values should replace A and B? \begin{tabular}{c|c|c|c|c|c} $x$ & -1 & 0 & 1 & 2 & 3 \\ \hline $y$ & -1 & A & 3 & B & 7 \end{tabular}

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Problem 7049

The equation of a line is $y=2 x+8$ What is the $y$ -intercept of the line?

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Problem 7050

The equation of a line is $y+4=6 x+11$
What is the value of $y$ at the point where the line crosses the $y$ -axis?

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Problem 7051

14. Solve. $x-9.5=-10.5$
Your answer

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Problem 7052

The Venn diagram below shows information about the number of items in sets $F$ and $G$ .
Given that there are fewer than 94 items in total, what is the largest possible number of items in set F?

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Problem 7053

$\begin{aligned} 3 v_{1}-2 v_{2}-3 v_{3} & =-6 \\ -12 v_{1}+19 v_{2}-3 v_{3} & =0 \\ -10 v_{1}-5 v_{2}+19 v_{3} & =140\end{aligned} \ldots$ (1)

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Problem 7054

$\begin{aligned} 3 v_{1}-2 v_{2}-3 v_{3} & =-6 \\ -12 v_{1}+19 v_{2}-3 v_{3} & =0 \\ -10 v_{1}-5 v_{2}+19 v_{3} & =140 \end{aligned} \ldots \text { (1) }$

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Problem 7055

Graph these equations: $\begin{array}{l} y=3 \\ y=4 \end{array}$
Click to select points on the graph. $y=3$ $y=4$
How many solutions does the system of equations have? no solution no solution one solution one solution infinitely many solutions Sctbmitit Work it out

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Problem 7056

$15-2(x+3)=x+9$

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Problem 7057

¿Cuál es una ecuación de la relación lineal en la forma pendiente-intercepto? $y=\square x-\square$

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Problem 7058

Bookwork code: 4H Calculator not allowed
In the pyramid, the number in the top brick is the sum of the numbers in the bottom two bricks. What number should replace $x$ ?

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Problem 7059

In 18-20, evaluate each expression for $x=1.8, x=5$ , and $x=6.4$ .
18. $x \div 4$
19. $x(3.35)$
20. $2 x+3.1$

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Problem 7060

18. The height of a pool increases by 4 cm for every 10 litres of water added.
After adding some water the height of the pool increased by 0.24 m . 18a. How many groups of 4 cm are there in 0.24 m ? Sets of $4 \mathrm{~cm}=6$
18b How much water was added to the pool? Amount of water $=$ Enter your next step here $\square$ litres

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Problem 7061

Solve the system of equations. $\begin{array}{l} y=6 x-8 \\ y=4 x+6 \end{array}$ $x=$ $\square$ $y=$

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Problem 7062

$14=3+2 x$

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Problem 7063

Whole Numbers Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. Micah is twice as old as Richard. Richard is three times as old as Ken. Ken is six years old. How old is Micah? 11 years old 8 years old 36 years old 18 years old

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Problem 7064

Progress:
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. How could you correctly rewrite the equation $4(5+3)=2(22-6)$ using the distributive property? $20+18=44-6$ $20+12=44-12$ $12+20=-12+44$ $20+3=44-6$

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Problem 7065

Yuto solved the equation below. $-2(x+5)=-2(x-2)+5$
What is the solution to Yuto's equation? $-10$ 9 no solution infinitely many solutions

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Problem 7066

A class of 204 students went on a field trip. They took 9 vehicles, some cars and some buses. Find the number of cars and the number of buses they took if each car holds 4 students and each bus hold 60 students.

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Problem 7067

ما هي العلاقة بين البُعد (Dimension) وعدد المتجهات المستقلة خطيًا في فضاء دعين؟

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Problem 7068

$2(x+2)+x=3(x-1)+6$
No solution $x=$ $\square$ All real numbers are solutions $-4(w+4)=3(w+4)+7$ No solution $w=$ $\square$ All real numbers are solutions Enolanation Check

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Problem 7069

yson wants to solve the inequality $\frac{1}{3} m<-21$ . How can he isolate the variable? Multiply both sides by 3 and reverse the inequality symbol. Multiply both sides by 3 and do not reverse the inequality symbol. Divide both sides by -21 and reverse the inequality symbol. Divide both sides by -21 and do not reverse the inequality symbol.

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Problem 7070

the equations. $9=\frac{5-k}{5}$

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Problem 7071

Solve the system of equations by the addition method. $\left\{\begin{array}{l} 3 x+2 y=3 \\ 9 x+6 y=0 \end{array}\right.$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $\square$ $\square$ ISimplify your answer Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

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Problem 7072

Which is the equation for the values in the table? 8.51 \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -10 & 10 & 20 & 30 \\ \hline $y$ & -7 & 3 & 8 & 13 \\ \hline \end{tabular}
A $y=-\frac{1}{2} x-2$ B $\quad y=-2 x+2$ C $y=2 x+2$ D $y=\frac{1}{2} x-2$

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Problem 7073

Write a function to describe the following scenario.
Joe is trying to fix a broken watch by figuring out how many seconds it is behind. He found that it began at 23 seconds behind and fell further behind by 2 seconds every hour. $y=[?]+\square x$

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Problem 7074

Solve for $x$ : $-(-x-1)=-x+3(-x+7)+6$

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Problem 7075

Find the slope of the line below.
Note: Enter negatives when necessary with no space between the negative sign and the number. If your answer is a fraction, enter your answer as a reduced improper fraction. Ex. $1 / 3$ for $\frac{2}{6}$ $\mathrm{m}=$ $\square$ type your answer...

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Problem 7076

7. $-34 b=272$
9. $65,600=160 j$
11. $-15 x=-120$

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Problem 7077

Solve the equation: $\frac{3 n-7}{6}=\frac{2 n+5}{3}$ .

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Problem 7078

How much will Karen have in her savings after 15 weeks if she starts with \ $20 and adds \$3 weekly? Use$ d + 15x$.

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Problem 7079

Find the equivalent expression for $\frac{1}{6}(30 x-24 y)-\frac{1}{8}(32 x-16 y)$ .

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Problem 7080

Solve for $x$ : $\frac{3 x}{6}+1=7$ . What is $x$ ? Options: $4$ , $12$ , $16$ .

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Problem 7081

Which equation matches $-4(x-5)+8x=9x-3$ ? A. $-5x=2$ B. $5x=-12$ C. $-5x=-23$ D. $5x=17$

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Problem 7082

Invest \$5,000 at 3% interest. How much to invest at 5% for total interest of \$275 after one year? Options: \$2,500, \$2,000, \$3,000.

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Problem 7083

Solve the equations: $6x=32$ and $6(x-8)=32$ .

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Problem 7084

After adding $3 x$ to $5 - 3 x = 2 x + 9$ , what should you do next? Options: add -9, add $-2 x$ , add -5.

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Problem 7085

Simplify the expression: $5 - y + 8$ .

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Problem 7086

Solve for $c$ in the equation: $-3c + 8 = -14$ .

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Problem 7087

Which set of ordered pairs $(x, y)$ represents a linear function:
A = {(0,5), (3,2), (6,-1), (10,-4)}, B = {(0,-1), (3,2), (0,5), (0,7)}, C = {(2,0), (4,0), (5,-3), (6,-5)}, D = {(-4,-5), (-1,1), (0,3), (4,6)}?

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Problem 7088

Solve for $c$ in the equation: $-3c + 8 = -19$ .

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Problem 7089

Which set of pairs $(x, y)$ represents a linear function: A, B, C, or D?

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Problem 7090

Which set of pairs $(x, y)$ represents a linear function? A, B, C, or D?

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Problem 7091

Which table shows a linear function? A: (0,6), (2,5), (5,2), (8,-1) B: (3,8), (5,4), (6,2), (8,0) C: (-6,-8), (-3,-5), (-1,-2), (2,1) D: (-6,-7), (-2,-1), (0,2), (4,8)

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Problem 7092

Which set of pairs $(x, y)$ represents a linear function: A, B, C, or D?

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Problem 7093

Which table shows a linear function? A: $(-3,-6), (0,-4), (3,-2), (6,0)$ ; B: $(-2,-7), (-1,-5), (0,-3), (2,-1)$ ; C: $(-6,6), (-2,0), (0,-3), (3,-6)$ ; D: $(2,0), (4,2), (6,3), (8,5)$ .

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Problem 7094

Which table shows a linear function? A: (-3,-5), (-1,-2), (1,1), (3,5); B: (-4,3), (-1,1), (2,-1), (8,-5); C: (1,-5), (3,-2), (5,2), (7,6); D: (-3,3), (-1,0), (2,-3), (5,-6).

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Problem 7095

Which set of pairs $(x, y)$ represents a linear function: A, B, C, or D?

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Problem 7096

Write a cost function for a ski resort charging \$20 plus \$4.25 per hour. Identify the variables used.

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Problem 7097

Solve for $y$ in the equation $4(y-3)=24$ .

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Problem 7098

Simplify $4(3 x+7)$ using the distributive property. Options: $7 x+7$ , $7 x+28$ , $12 x+7$ , $12 x+28$ .

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Problem 7099

Simplify $\frac{1}{2}(8 x-16)$ using the distributive property. Options: 4 x-8, 4 x-16, 16 x-8, 16 x-32.

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Problem 7100

Identify the equation for: The sum of 12 and a number equals 4 times the number. $12+n=4 n$ $12+4 n=n$ $12 n=4+n$ $12(n+4)=n$

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1 ...68 69 70 71 72 73 74 ...77

Linearity

Problem 7001

For each value of yyy, check if it satisfies 3y+4≥−143y + 4 \geq -143y+4≥−14. Values: -9, 2, -3, -6.

Problem 7002

Solve the compound inequality: 5<3x+2<175 < 3x + 2 < 175<3x+2<17 and graph the solution on a number line.

Problem 7003

Check if each xxx satisfies the inequality 69≤7x+669 \leq 7x + 669≤7x+6. Is it a solution? (Yes/No) for x=10,−6,9,2x = 10, -6, 9, 2x=10,−6,9,2.

Problem 7004

Translate to an inequality: 2y−4≥−292y - 4 \geq -292y−4≥−29.

Problem 7005

Find kkk in y=kxy=kxy=kx and complete the values for yyy when xxx is 1, 4, 6, 10, 11, and 15.

Problem 7006

Solve the compound inequality: 3≤14x+4<53 \leq \frac{1}{4} x + 4 < 53≤41​x+4<5.

Problem 7007

Choose the correct solution for each inequality and provide the answer if applicable. (a) 5(3−u)+5u>175(3-u)+5u>175(3−u)+5u>17 (b) −2(v+6)+28≤4(3−v)-2(v+6)+28 \leq 4(3-v)−2(v+6)+28≤4(3−v)

Problem 7008

Solve the system by the elimination method. 6x=3y−25x+1=7y\begin{array}{l} 6 x=3 y-2 \\ 5 x+1=7 y \end{array}6x=3y−25x+1=7y​

Problem 7009

7/327 / 327/32 A line is perpendicular to y=2x−7\mathrm{y}=2 \mathrm{x}-7y=2x−7. What is the slope of this line? −1/2-1 / 2−1/2 −2-2−2 2 1/21 / 21/2

Problem 7010

8. Which of the following equations is perpendicular to the line 2x+3y=62 x+3 y=62x+3y=6 ? a. y=−12x+4y=-\frac{1}{2} x+4y=−21​x+4 c. y=−32x+1y=-\frac{3}{2} x+1y=−23​x+1 b. y=32x−1y=\frac{3}{2} x-1y=23​x−1 d. y=2x+3y=2 x+3y=2x+3

Problem 7011

Give the slope between the points (−4,−2)(5,−13)(-4,-2) \quad(5,-13)(−4,−2)(5,−13) OK

Problem 7012

What is the value of yyy ? 9y=279y9=279\begin{array}{l} 9 y=27 \\ \frac{9 y}{9}=\frac{27}{9} \end{array}9y=2799y​=927​​ y=y=y=

Problem 7013

- Higher LevelIlowing simultaneous equations for x,y,w∈Zx, y, w \in \mathbb{Z}x,y,w∈Z : x+2y=143y+3w=−744x+5w=4\begin{aligned} x+2 y & =143 \\ y+3 w & =-74 \\ 4 x+5 w & =4 \end{aligned}x+2yy+3w4x+5w​=143=−74=4​

Problem 7014

The graph of linear function fff passes through the point (1,−9)(1,-9)(1,−9) and has a slope of -3 .What is the zero of fff ?F 2 G 4 H -6 J -2

Problem 7015

Problem 7016

57. −5>p−15-5>p-\frac{1}{5}−5>p−51​

Problem 7017

Is y−4=3(x+1)y-4=3(x+1)y−4=3(x+1) an equation of a line through (−2,1)(-2,1)(−2,1) ? Explain.

Problem 7018

Problem 7019

11. Miguel's paycheck is $871.25\$ 871.25$871.25. The paycheck includes 36.5 hours of work and a $50\$ 50$50 bonus. How much does Miguel earn for each hour of work, not including the bonus?

Problem 7020

B) Graph the inequality. 3x−2y<183 x-2 y<183x−2y<18

Problem 7021

Solve the compound inequality: 4y+3≥194y + 3 \geq 194y+3≥19 and 2y+2≥−42y + 2 \geq -42y+2≥−4. Provide the solution in interval notation.

Problem 7022

Solve the inequality: −4x≥8-4x \geq 8−4x≥8 or 2x−2>82x - 2 > 82x−2>8. Provide the solution in interval notation or as ∅\varnothing∅.

Problem 7023

Solve and justify the first step for: 1. x+4+3x=72x + 4 + 3x = 72x+4+3x=72; 2. x+3+x−8+x=55x + 3 + x - 8 + x = 55x+3+x−8+x=55.

Problem 7024

Solve x+3+x−8+x=55x + 3 + x - 8 + x = 55x+3+x−8+x=55. What property justifies your first step?

Problem 7025

Solve x+3+x−8+x=55x+3+x-8+x=55x+3+x−8+x=55 and 12x+10=14x+54\frac{1}{2} x+10=\frac{1}{4} x+5421​x+10=41​x+54. Explain your first step and its justification.

Problem 7026

Solve 12x+10=14x+54\frac{1}{2} x+10=\frac{1}{4} x+5421​x+10=41​x+54. Explain your first step and the property used.

Problem 7027

Solve x+x+24=189.5\frac{x+x+2}{4}=189.54x+x+2​=189.5. Explain the property used for your first step and your reasoning.

Problem 7028

Solve the equation 14x+18=x\frac{1}{4} x + 18 = x41​x+18=x and explain the property used for your first step.

Problem 7029

Thu is 5 years older than Tuan. Their ages add up to 51. Find their ages: T+(T+5)=51T + (T + 5) = 51T+(T+5)=51.

Problem 7030

Tomás thinks of a number. If he triples it and subtracts 13, he gets 305. What is the number? Solve: 3x−13=3053x - 13 = 3053x−13=305.

Problem 7031

Find two consecutive numbers whose sum is 123. What are the numbers?

Problem 7032

Find two consecutive even numbers that add up to 246.

Problem 7033

Find two consecutive even numbers that add up to 246. What are the numbers?

Problem 7034

Alysha solved 2x−3−8x=14+2x−12 x-3-8 x=14+2 x-12x−3−8x=14+2x−1. Find her mistake and solve the equation correctly. What is xxx?

Problem 7035

Joe's age is 3 times Aaron's. Aaron is 6 years older than Christina. Their ages sum to 149. Find Christina's, Joe's, and Aaron's ages.

Problem 7036

Solve for yyy in the equation: −5=9+y-5=9+y−5=9+y.

Problem 7037

Solve for nnn in the equation n+24=1\frac{n+2}{4}=14n+2​=1.

Problem 7038

Luke swims at 3 m/s. What is the slope of the line on a graph with time on the xxx-axis and distance on the yyy-axis? Distance in 45 seconds is (45, ).

Problem 7039

Evaluate −73x+10-\frac{7}{3} x + 10−37​x+10 when x=6x = 6x=6.

Problem 7040

Calculate the slope between the points (18,-12) and (-11,17). Use the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

Problem 7041

For each value of $y$ , check if it satisfies $3y + 4 \geq -14$ . Values: -9, 2, -3, -6.

Solve the compound inequality: $5 < 3x + 2 < 17$ and graph the solution on a number line.

Check if each $x$ satisfies the inequality $69 \leq 7x + 6$ . Is it a solution? (Yes/No) for $x = 10, -6, 9, 2$ .

Translate to an inequality: $2y - 4 \geq -29$ .

Find $k$ in $y=kx$ and complete the values for $y$ when $x$ is 1, 4, 6, 10, 11, and 15.

Solve the compound inequality: $3 \leq \frac{1}{4} x + 4 < 5$ .

Choose the correct solution for each inequality and provide the answer if applicable. (a) $5(3-u)+5u>17$ (b) $-2(v+6)+28 \leq 4(3-v)$

Solve the system by the elimination method. $\begin{array}{l} 6 x=3 y-2 \\ 5 x+1=7 y \end{array}$

$7 / 32$ A line is perpendicular to $\mathrm{y}=2 \mathrm{x}-7$ . What is the slope of this line? $-1 / 2$ $-2$ 2 $1 / 2$

8. Which of the following equations is perpendicular to the line $2 x+3 y=6$ ? a. $y=-\frac{1}{2} x+4$ c. $y=-\frac{3}{2} x+1$ b. $y=\frac{3}{2} x-1$ d. $y=2 x+3$

Give the slope between the points $(-4,-2) \quad(5,-13)$ OK

What is the value of $y$ ? $\begin{array}{l} 9 y=27 \\ \frac{9 y}{9}=\frac{27}{9} \end{array}$ $y=$

- Higher Level
Ilowing simultaneous equations for $x, y, w \in \mathbb{Z}$ : $\begin{aligned} x+2 y & =143 \\ y+3 w & =-74 \\ 4 x+5 w & =4 \end{aligned}$

The graph of linear function $f$ passes through the point $(1,-9)$ and has a slope of -3 .
What is the zero of $f$ ?
F 2 G 4 H -6 J -2

57. $-5>p-\frac{1}{5}$

Is $y-4=3(x+1)$ an equation of a line through $(-2,1)$ ? Explain.

11. Miguel's paycheck is $\$ 871.25$ . The paycheck includes 36.5 hours of work and a $\$ 50$ bonus. How much does Miguel earn for each hour of work, not including the bonus?

B) Graph the inequality. $3 x-2 y<18$

Solve the compound inequality: $4y + 3 \geq 19$ and $2y + 2 \geq -4$ . Provide the solution in interval notation.

Solve the inequality: $-4x \geq 8$ or $2x - 2 > 8$ . Provide the solution in interval notation or as $\varnothing$ .

Solve and justify the first step for: 1. $x + 4 + 3x = 72$ ; 2. $x + 3 + x - 8 + x = 55$ .

Solve $x + 3 + x - 8 + x = 55$ . What property justifies your first step?

Solve $x+3+x-8+x=55$ and $\frac{1}{2} x+10=\frac{1}{4} x+54$ . Explain your first step and its justification.

Solve $\frac{1}{2} x+10=\frac{1}{4} x+54$ . Explain your first step and the property used.

Solve $\frac{x+x+2}{4}=189.5$ . Explain the property used for your first step and your reasoning.

Solve the equation $\frac{1}{4} x + 18 = x$ and explain the property used for your first step.

Thu is 5 years older than Tuan. Their ages add up to 51. Find their ages: $T + (T + 5) = 51$ .

Tomás thinks of a number. If he triples it and subtracts 13, he gets 305. What is the number? Solve: $3x - 13 = 305$ .

Alysha solved $2 x-3-8 x=14+2 x-1$ . Find her mistake and solve the equation correctly. What is $x$ ?

Solve for $y$ in the equation: $-5=9+y$ .

Solve for $n$ in the equation $\frac{n+2}{4}=1$ .

Luke swims at 3 m/s. What is the slope of the line on a graph with time on the $x$ -axis and distance on the $y$ -axis? Distance in 45 seconds is (45, ).

Evaluate $-\frac{7}{3} x + 10$ when $x = 6$ .

Calculate the slope between the points (18,-12) and (-11,17). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Find the slope-intercept form of the line passing through $(-1,1)$ with a slope of $0$ .

Find the slope-intercept form of the line that passes through the points $(2,3)$ and $(4,2)$ .

Write an inequality for: The product of $2x$ and $16$ is at most $9$ .

$\frac{5 x-3}{2}=6$

Question 2: solve the system of equations by graphical method: $\begin{array}{l} \mathrm{x}+2 \mathrm{y}=4 \\ \mathrm{y}=\frac{-1}{2} x+2 \end{array}$

Copy and complete the table below for the graph of $y=2 x+1$ . What values should replace A and B? \begin{tabular}{c|c|c|c|c|c} $x$ & -1 & 0 & 1 & 2 & 3 \\ \hline $y$ & -1 & A & 3 & B & 7 \end{tabular}

The equation of a line is $y=2 x+8$ What is the $y$ -intercept of the line?

The equation of a line is $y+4=6 x+11$
What is the value of $y$ at the point where the line crosses the $y$ -axis?

14. Solve. $x-9.5=-10.5$
Your answer

The Venn diagram below shows information about the number of items in sets $F$ and $G$ .
Given that there are fewer than 94 items in total, what is the largest possible number of items in set F?

Graph these equations: $\begin{array}{l} y=3 \\ y=4 \end{array}$
Click to select points on the graph. $y=3$ $y=4$
How many solutions does the system of equations have? no solution no solution one solution one solution infinitely many solutions Sctbmitit Work it out

$15-2(x+3)=x+9$

¿Cuál es una ecuación de la relación lineal en la forma pendiente-intercepto? $y=\square x-\square$

Bookwork code: 4H Calculator not allowed
In the pyramid, the number in the top brick is the sum of the numbers in the bottom two bricks. What number should replace $x$ ?

In 18-20, evaluate each expression for $x=1.8, x=5$ , and $x=6.4$ .
18. $x \div 4$
19. $x(3.35)$
20. $2 x+3.1$

Solve the system of equations. $\begin{array}{l} y=6 x-8 \\ y=4 x+6 \end{array}$ $x=$ $\square$ $y=$

$14=3+2 x$

Yuto solved the equation below. $-2(x+5)=-2(x-2)+5$
What is the solution to Yuto's equation? $-10$ 9 no solution infinitely many solutions

$2(x+2)+x=3(x-1)+6$
No solution $x=$ $\square$ All real numbers are solutions $-4(w+4)=3(w+4)+7$ No solution $w=$ $\square$ All real numbers are solutions Enolanation Check

the equations. $9=\frac{5-k}{5}$

Write a function to describe the following scenario.
Joe is trying to fix a broken watch by figuring out how many seconds it is behind. He found that it began at 23 seconds behind and fell further behind by 2 seconds every hour. $y=[?]+\square x$

Solve for $x$ : $-(-x-1)=-x+3(-x+7)+6$