Question

How do you solve `2(x+6)=-2(x-4)`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on each side of the equation:

`(2 xx x) + (2 xx 6) = (-2 xx x) - (-2 xx 4)`

`2x + 12 = -2x - (-8)`

`2x + 12 = -2x + 8`

Next, subtract `color(red)(12)` and add `color(blue)(2x)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`2x + 12 - color(red)(12) + color(blue)(2x) = -2x + 8 - color(red)(12) + color(blue)(2x)`

`2x + color(blue)(2x) + 12 - color(red)(12) = -2x + color(blue)(2x) + 8 - color(red)(12)`

`(2 + color(blue)(2))x + 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`

Answer 2

`x=-1`

Explanation:

Let's distribute the `2` on the left, and the `-2` on the right to get

`2x+12=-2x+8`

Next, let's add `2x` to both sides to get

`4x+12=8`

Let's subtract `12` from both sides to get

`4x=-4`

Lastly, we can divide both sides by `4` to get

`x=-1`