Math  /  Algebra

QuestionMTH1 W1, Unit 5- Solving Equations and Word Problems
Lesson 1- Homework Solve each equation in the space provided. Show work-properly, carefully, and neatly! ! a) 5x=37+85 x=37+8 x=256x=5x=\frac{25}{6} \quad x=5. d) g) 5x2+x=9+3x+105 x-2+x=9+3 x+10 h) b) 4x+9=114 x+9=-11 9x=11.9x=204=5\begin{array}{l} 9 x=-11.9 \\ x=\frac{-20}{4}=-5 \end{array} e) e) \quad f) 87x=417x=4187x=49x=497x=77x=4187x=49x=497x=77x=4187x=49x=49x=7 c) 2x\begin{array}{l} 8-7 x=-41 \\ \begin{array}{r} -7 x=-41-8 \\ -7 x=-49 \\ x=\frac{-49}{-7} \\ x=7 \end{array} \\ \begin{array}{r} -7 x=-41-8 \\ -7 x=-49 \\ x=\frac{-49}{-7} \\ x=7 \end{array} \\ \begin{aligned} -7 x & =-41-8 \\ -7 x & =-49 \\ x & =-49 \\ x & =7 \end{aligned} \\ \text { c) } \\ -2 x \end{array} 7x5=6x+69x+4=8x37 x-5=6 x+6 \quad 9 x+4=8 x-3 7x6x+57 x-6 x+5 i) 5x+5x=7+x25 x+5-x=-7+x-2
Solutions a)5 b) -5 c) 7 d) -7 e) 11 f) -7 g)7 h) 143\frac{-14}{3} i) 52\frac{5}{2}

Studdy Solution

STEP 1

What is this asking? We need to solve a bunch of single-variable equations, showing all the fantastic work! Watch out! Don't rush!
It's easy to make mistakes with signs when adding, subtracting, multiplying, or dividing.
Also, remember to keep your work organized.

STEP 2

1. Solve equation (g)

STEP 3

The equation we're tackling is 5x2+x=9+3x+105x - 2 + x = 9 + 3x + 10.
Let's do this!

STEP 4

On the left side, we have 5x5x and xx.
Adding them gives us 6x6x.
So, the left side becomes 6x26x - 2.
On the right side, we have 99 and 1010.
Adding those together gives us 1919.
The right side becomes 19+3x19 + 3x.
Now our equation is 6x2=19+3x6x - 2 = 19 + 3x.

STEP 5

Let's get all the xx terms on one side.
We can subtract 3x3x from both sides of the equation. 6x3x6x - 3x gives us 3x3x, and 3x3x3x - 3x adds to zero.
Our equation is now 3x2=193x - 2 = 19.

STEP 6

Now, let's move that 2-2 to the other side.
We can do this by adding 22 to both sides of the equation. 2+2-2 + 2 adds to zero, and 19+219 + 2 is 2121.
This simplifies our equation to 3x=213x = 21.

STEP 7

Finally, to get xx all by itself, we divide both sides by 33. 3x3x divided by 33 is xx, and 2121 divided by 33 is 77.
So, x=7x = 7!

STEP 8

The solution to equation (g) is x=7x = 7.

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