Question

How do you solve `9(x-3)=5x+2`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the left side of the equation:

`(9 xx x) - (9 xx 3) = 5x + 2`

`9x - 27 = 5x + 2`

Next, add `color(red)(27)` and subtract `color(blue)(5x)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`9x - 27 + color(red)(27) - color(blue)(5x) = 5x + 2 + color(red)(27) - color(blue)(5x)`

`9x - color(blue)(5x) - 27 + color(red)(27) = 5x - color(blue)(5x + 2 + color(red)(27))`

`4x - 0 = 0 + 29`

`4x = 29`

Now, divide each side of the equation by `color(red)(4)` to solve for `x` while keeping the equation balanced:

`(4x)/color(red)(4) = 29/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 29/4`

`x = 29/4`