Question

How do you solve `2(x-1) + 3= x -3(x+1)`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis on each side of the equation by multiplying each term inside the parenthesis by the term outside the parenthesis:

`color(red)(2)(x - 1) + 3 = x - color(blue)(3)(x + 1)`

`(color(red)(2) xx x) - (color(red)(2) xx 1) + 3 = x - (color(blue)(3) xx x) - (color(blue)(3) xx 1)`

`2x - 2 + 3 = x - 3x - 3`

`2x + 1 = -2x - 3`

Next, subtract `color(red)(1)` and add `color(blue)(2x)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`color(blue)(2x) + 2x + 1 - color(red)(1) = color(blue)(2x) - 2x - 3 - color(red)(1)`

`4x + 0 = 0 - 4`

`4x = -4`

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

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

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = -1`

`x = -1`