Question

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

Answer 1

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`

Answer 2

`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