Question

How do you solve `3( x + 9) = - 3( 8x - 7) + 9x`?

Answer 1

`x=(-1)/3`

Explanation:

`3(x+9)=-3(8x-7)+9x`

Let's start by using the distributive property*

`(3)(x)+(3)(9)=(-3)(8x)+(-3)(-7)+9x`

`3x + 27 = -24x + 21 + 9x`

`3x + 27= -15x + 21`

Subtract `color(red)(27)` from both sides

`3x cancel(+ 27 - color(red)(27))=15x + 21 - color(red)(27)`

`3x = -15x -6`

Add `15x` to both sides

`3x + 15x=cancel(-15x + 15x) -6`

`18x = -6`

Finally, divide both sides by `18`

`(cancel18x)/cancel18 = 6/18`

`x=(-1)/3`

Answer 2

`x=-1/2`

Explanation:

We can divide both sides by `3` to get

`x+9=-(8x-7)+3x`

Next, we can distribute the negative on the right to get

`x+9=-8x+7+3x`

Combining the `x` terms on the right gives us

`x+9=-5x+7`

Next, add `5x` to both sides to get

`6x+9=7`

Next, subtract `9` from both sides to get

`6x=-3`

Dividing both sides by `6` gives us

`x=-1/2`

Hope this helps!