Question

How do you solve `-3(x-1)+9=15`?

Answer 1

`x = -1`

Explanation:

The first step is to expand the terms in parenthesis by multiplying each term within the parenthesis by `color(red)(-3)` being careful to ensure the sign of the product is correct:

`(color(red)(-3) * x) + (color(red)(-3) * - 1) + 9 = 15`

`-3x + 3 + 9 = 15`

Next we can combine the like terms on the left side of the equation:

`-3x + (3 + 9) = 15`

`-3x + 12 = 15`

Then, we can subtract `color(blue)(12)` from each side of the equation to isolate the `x` term and keep the equation balanced:

`-3x + 12 -color(blue)(12) = 15 - color(blue)(12)`

`-3x + 0 = 3`

`-3x = 3`

Now, we can divide each side of the equation by `color(green)(-3)` to solve for `x` and keep the equation balanced:

`(-3x)/color(green)(-3) = 3/color(green)(-3)`

`(color(green)(cancel(color(black)(-3)))x)/cancel(color(green)(-3)) = -1`

`x = -1`