Math / Algebra

QuestionMath $2 A$ REVIEW SHOW ALL WORK Unit 5 Module 9 Linear Equations and Inequalities Name $\qquad$ Datel Per $\qquad$ LT SA: I can solve and write multi-step equations that intudo declmbls and froctions. I can solve the eral equaktons. 1) Solve the equation for $x$ . 2) Solve the equation for $x$ . $7 x+8(x-3)=12-3 x$ $14.3 h-6.5 h=10.3 h+9$

Studdy Solution

STEP 1

What is this asking? We've got two equations, and we need to find the value of $x$ that makes the first one true, and the value of $h$ that makes the second one true! Watch out! Don't forget to distribute correctly and combine like terms carefully.
Keep track of those negative signs!

STEP 2

1. Solve the first equation
2. Solve the second equation

STEP 3

Alright, let's start with the first equation: $7x + 8(x - 3) = 12 - 3x$ .
First, we need to distribute that 8 to both terms inside the parentheses.
Think of it like sharing the 8 with both the $x$ and the $-3$ .

STEP 4

So, $8$ times $x$ gives us $8x$ , and $8$ times $-3$ gives us $-24$ .
Now our equation looks like this: $7x + 8x - 24 = 12 - 3x$ .

STEP 5

Now, let's combine those $x$ terms on the left side.
We have $7x$ and $8x$ , and adding them together gives us $15x$ .
So, our equation becomes $15x - 24 = 12 - 3x$ .

STEP 6

Let's get all the $x$ terms on one side.
We can do this by adding $3x$ to both sides of the equation.
This gives us $15x + 3x - 24 = 12 - 3x + 3x$ , which simplifies to $18x - 24 = 12$ .

STEP 7

Now, let's isolate the $x$ term by adding 24 to both sides: $18x - 24 + 24 = 12 + 24$ .
This simplifies to $18x = 36$ .

STEP 8

Finally, we divide both sides by 18 to solve for $x$ : $\frac{18x}{18} = \frac{36}{18}$ .
This gives us $x = 2$ .
Awesome!

STEP 9

Let's tackle the second equation: $14.3h - 6.5h = 10.3h + 9$ .
First, we'll combine the $h$ terms on the left side: $14.3h - 6.5h$ gives us $7.8h$ .
So, our equation is now $7.8h = 10.3h + 9$ .

STEP 10

Now, let's move that $10.3h$ to the left side by subtracting it from both sides: $7.8h - 10.3h = 10.3h - 10.3h + 9$ .
This simplifies to $-2.5h = 9$ .

STEP 11

Lastly, we divide both sides by $-2.5$ to find $h$ : $\frac{-2.5h}{-2.5} = \frac{9}{-2.5}$ .
This gives us $h = -3.6$ .
Fantastic!

STEP 12

For the first equation, we found $x = 2$ .
For the second equation, we found $h = -3.6$ .
We did it!

Was this helpful?

Studdy Solution

STEP 1

What is this asking? We've got two equations, and we need to find the value of $x$ that makes the first one true, and the value of $h$ that makes the second one true! Watch out! Don't forget to distribute correctly and combine like terms carefully.
Keep track of those negative signs!

STEP 2

1. Solve the first equation
2. Solve the second equation

STEP 3

Alright, let's start with the first equation: $7x + 8(x - 3) = 12 - 3x$ .
First, we need to distribute that 8 to both terms inside the parentheses.
Think of it like sharing the 8 with both the $x$ and the $-3$ .

STEP 4

So, $8$ times $x$ gives us $8x$ , and $8$ times $-3$ gives us $-24$ .
Now our equation looks like this: $7x + 8x - 24 = 12 - 3x$ .

STEP 5

Now, let's combine those $x$ terms on the left side.
We have $7x$ and $8x$ , and adding them together gives us $15x$ .
So, our equation becomes $15x - 24 = 12 - 3x$ .

STEP 6

Let's get all the $x$ terms on one side.
We can do this by adding $3x$ to both sides of the equation.
This gives us $15x + 3x - 24 = 12 - 3x + 3x$ , which simplifies to $18x - 24 = 12$ .

STEP 7

Now, let's isolate the $x$ term by adding 24 to both sides: $18x - 24 + 24 = 12 + 24$ .
This simplifies to $18x = 36$ .

STEP 8

Finally, we divide both sides by 18 to solve for $x$ : $\frac{18x}{18} = \frac{36}{18}$ .
This gives us $x = 2$ .
Awesome!

STEP 9

Let's tackle the second equation: $14.3h - 6.5h = 10.3h + 9$ .
First, we'll combine the $h$ terms on the left side: $14.3h - 6.5h$ gives us $7.8h$ .
So, our equation is now $7.8h = 10.3h + 9$ .

STEP 10

Now, let's move that $10.3h$ to the left side by subtracting it from both sides: $7.8h - 10.3h = 10.3h - 10.3h + 9$ .
This simplifies to $-2.5h = 9$ .

STEP 11

Lastly, we divide both sides by $-2.5$ to find $h$ : $\frac{-2.5h}{-2.5} = \frac{9}{-2.5}$ .
This gives us $h = -3.6$ .
Fantastic!

STEP 12

For the first equation, we found $x = 2$ .
For the second equation, we found $h = -3.6$ .
We did it!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? We've got two equations, and we need to find the value of xxx that makes the first one true, and the value of hhh that makes the second one true! Watch out! Don't forget to distribute correctly and combine like terms carefully.Keep track of those negative signs!

STEP 2

1. Solve the first equation2. Solve the second equation

STEP 3

Alright, let's **start** with the first equation: 7x+8(x−3)=12−3x7x + 8(x - 3) = 12 - 3x7x+8(x−3)=12−3x.First, we need to **distribute** that 8 to both terms inside the parentheses.Think of it like sharing the 8 with both the xxx and the −3-3−3.

STEP 4

So, 888 times xxx gives us 8x8x8x, and 888 times −3-3−3 gives us −24-24−24.Now our equation looks like this: 7x+8x−24=12−3x7x + 8x - 24 = 12 - 3x7x+8x−24=12−3x.

STEP 5

Now, let's **combine** those xxx terms on the left side.We have 7x7x7x and 8x8x8x, and adding them together gives us 15x15x15x.So, our equation becomes 15x−24=12−3x15x - 24 = 12 - 3x15x−24=12−3x.

STEP 6

Let's **get all the** xxx **terms** on one side.We can do this by adding 3x3x3x to both sides of the equation.This gives us 15x+3x−24=12−3x+3x15x + 3x - 24 = 12 - 3x + 3x15x+3x−24=12−3x+3x, which simplifies to 18x−24=1218x - 24 = 1218x−24=12.

STEP 7

Now, let's **isolate** the xxx term by adding 24 to both sides: 18x−24+24=12+2418x - 24 + 24 = 12 + 2418x−24+24=12+24.This simplifies to 18x=3618x = 3618x=36.

STEP 8

Finally, we **divide** both sides by 18 to solve for xxx: 18x18=3618\frac{18x}{18} = \frac{36}{18}1818x​=1836​.This gives us x=2x = 2x=2.Awesome!

STEP 9

Let's **tackle** the second equation: 14.3h−6.5h=10.3h+914.3h - 6.5h = 10.3h + 914.3h−6.5h=10.3h+9.First, we'll **combine** the hhh terms on the left side: 14.3h−6.5h14.3h - 6.5h14.3h−6.5h gives us 7.8h7.8h7.8h.So, our equation is now 7.8h=10.3h+97.8h = 10.3h + 97.8h=10.3h+9.

STEP 10

Now, let's **move** that 10.3h10.3h10.3h to the left side by subtracting it from both sides: 7.8h−10.3h=10.3h−10.3h+97.8h - 10.3h = 10.3h - 10.3h + 97.8h−10.3h=10.3h−10.3h+9.This simplifies to −2.5h=9-2.5h = 9−2.5h=9.

STEP 11

Lastly, we **divide** both sides by −2.5-2.5−2.5 to find hhh: −2.5h−2.5=9−2.5\frac{-2.5h}{-2.5} = \frac{9}{-2.5}−2.5−2.5h​=−2.59​.This gives us h=−3.6h = -3.6h=−3.6.Fantastic!

STEP 12

For the first equation, we found x=2x = 2x=2.For the second equation, we found h=−3.6h = -3.6h=−3.6.We did it!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We've got two equations, and we need to find the value of $x$ that makes the first one true, and the value of $h$ that makes the second one true! Watch out! Don't forget to distribute correctly and combine like terms carefully.
Keep track of those negative signs!

1. Solve the first equation
2. Solve the second equation

Alright, let's start with the first equation: $7x + 8(x - 3) = 12 - 3x$ .
First, we need to distribute that 8 to both terms inside the parentheses.
Think of it like sharing the 8 with both the $x$ and the $-3$ .

So, $8$ times $x$ gives us $8x$ , and $8$ times $-3$ gives us $-24$ .
Now our equation looks like this: $7x + 8x - 24 = 12 - 3x$ .

Now, let's combine those $x$ terms on the left side.
We have $7x$ and $8x$ , and adding them together gives us $15x$ .
So, our equation becomes $15x - 24 = 12 - 3x$ .

Let's get all the $x$ terms on one side.
We can do this by adding $3x$ to both sides of the equation.
This gives us $15x + 3x - 24 = 12 - 3x + 3x$ , which simplifies to $18x - 24 = 12$ .

Now, let's isolate the $x$ term by adding 24 to both sides: $18x - 24 + 24 = 12 + 24$ .
This simplifies to $18x = 36$ .

Finally, we divide both sides by 18 to solve for $x$ : $\frac{18x}{18} = \frac{36}{18}$ .
This gives us $x = 2$ .
Awesome!

Let's tackle the second equation: $14.3h - 6.5h = 10.3h + 9$ .
First, we'll combine the $h$ terms on the left side: $14.3h - 6.5h$ gives us $7.8h$ .
So, our equation is now $7.8h = 10.3h + 9$ .

Now, let's move that $10.3h$ to the left side by subtracting it from both sides: $7.8h - 10.3h = 10.3h - 10.3h + 9$ .
This simplifies to $-2.5h = 9$ .

Lastly, we divide both sides by $-2.5$ to find $h$ : $\frac{-2.5h}{-2.5} = \frac{9}{-2.5}$ .
This gives us $h = -3.6$ .
Fantastic!

For the first equation, we found $x = 2$ .
For the second equation, we found $h = -3.6$ .
We did it!