Question

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

Answer 1

`x = -1`

Explanation:

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

First, use the distributive property to simplify `2(x-1)` and `-3(x+1)`:

Following this image, we know that:
`color(blue)(2(x-1) = (2 * x) + (2 * -1) = 2x - 1)`
and
`color(blue)(-3(x+1) = (-3 * x) + (-3 * 1) = -3x + -3)`

Put them back into the equation:
`2x - 2 + 3 = x - 3x - 3`

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

Add `color(blue)(2x)` to both sides of the equation:
`2x + 1 quadcolor(blue)(+quad2x) = -2x - 3 quadcolor(blue)(+quad2x)`

`4x + 1 = -3`

Subtract `color(blue)1` from both sides of the equation:
`4x + 1 quadcolor(blue)(-quad1) = -3 quadcolor(blue)(-quad1)`

`4x = -4`

Divide both sides by `color(blue)4`:
`(4x)/color(blue)4 = -4/color(blue)4`

Therefore,
`x = -1`

Hope this helps!