How do you solve 9(2 - 3x) - 29 = 8x + 23 - x?

2 Answers
Jan 8, 2018

See a solution process below:

Explanation:

First rewrite the expression as:

9(2 - 3x) - 29 = 8x - x + 23

Next, expand the term in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

color(red)(9)(2 - 3x) - 29 = 8x - x + 23

(color(red)(9) xx 2) - (color(red)(9) xx 3x) - 29 = 8x - x + 23

18 - 27x - 29 = 8x - x + 23

Then, group and combine like terms on each side of the equation:

18 - 29 - 27x = 8x - x + 23

-11 - 27x = (8 - 1)x + 23

-11 - 27x = 7x + 23

Next, add color(red)(27x) and subtract color(blue)(23) from each side of the equation to isolate the x term while keeping the equation balanced:

-11 - color(blue)(23) - 27x + color(red)(27x) = 7x + color(red)(27x) + 23 - color(blue)(23)

-34 - 0 = (7 + color(red)(27))x + 0

-34 = 34x

Now, divide each side of the equation by color(red)(34) to solve for x while keeping the equation balanced:

-34/color(red)(34) = (34x)/color(red)(34)

-1 = (color(red)(cancel(color(black)(34)))x)/cancel(color(red)(34))

-1 = x

x = -1

Jan 8, 2018

x=-1

Explanation:

Ok, so there are a few steps to this problem. First we need to combine like terms. Then we will subtract the lowest term from both sides. Let me explain:

We begin with the problem

9(2-3x)-29=8x-(x-23)

We need o get rid of the parentheses. To do this we just multiply everything in the parentheses by whats outside of them

18-27x-29=8x-x+23

Now we need to combine like terms

-27x-11=7x+23

Ok, finally, we need to get x on one side with (hopefully) the answer on the other

(Subtract 7x)
-27x-11-7x=cancel(7x)+23cancel(-7x)

-34x-11=23

(Add 11)
-34xcancel(-11)+cancel(11)=23+11

-34x=34

(Divide by -34)
(cancel(-34x))/cancel(-34)=34/-34

x=-1

Hope this helped!
~Chandler Dowd