Question

How do you solve `-15x - 40= 9- 8x`?

Answer 1

`color(green)(x=7)`

Explanation:

Given
`color(white)("XXX")-15x-40=9-8x`

Add `8x+40(=40+8x)` to both sides in order to isolate the variable term on the left and the constant term on the right:
`color(white)("XXX")-15x-40=color(white)("x")9-8x`
`color(white)("XXX")+color(white)("x")underline(8x+40)=underline(40+8x)`
`color(white)("XXXX")-7xcolor(white)("xxxx")=49`

Divide both sides by `(-7)`
`color(white)("XXXXXX")xcolor(white)("xxxx")=7`

Answer 2

See the entire solution process below:

Explanation:

First, add `color(red)(15x)` and subtract `color(blue)(9)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-15x - 40 + color(red)(15x) - color(blue)(9) = 9 - 8x + color(red)(15x) - color(blue)(9)`

`-15x + color(red)(15x) - 40 - color(blue)(9) = 9 - color(blue)(9) - 8x + color(red)(15x)`

`0 - 49 = 0 + 7x`

`-49 = 7x`

Now, divide each side of the equation by `color(red)(7)` to solve for `x` while keeping the equation balanced:

`-49/color(red)(7) = (7x)/color(red)(7)`

`-7 = (color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7))`

`-7 = x`

`x = -7`