Question

How do you solve `3(x + 1) = -2(x - 1) - 4`?

Answer 1

`3(x+1) = 2(-x+1)-4`
`3x + 3 = -2x + 2 -4`
`3x + 3 = -2x -2`
`5x = -5`
`x = -1`

Explanation:

First you need to expand out the brackets on both sides of the equals sign.

`3(x+1)`
`3x + 3`

Times the `3` on the outside of the first set of brackets by `x` and then by `1`. This makes `3x + 3.`

Now expand the second set of brackets out. Remember that the `-4` has nothing to do with this set of brackets.

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

Here, you times `2` by `-x`. This makes `-2x`. Then you times `2` by `+1`. This makes `+2`.

Now write out the sum with the newly expanded brackets and the `-4`.

`3x + 3 = -2x + 2 -4`

Collect the like terms on each side of the equals sign to make:

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

I did the sum `+2 - 4` to work this out.

Now you have to collect all the `x`'s on one side and the other numbers on the other side.

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

To cancel out `-2x` you must `+2x` on each side of the equals sign.

`5x + 3 = -2`

Then, to get rid of the `+3` on the left side of the equals sign, you must `-3` from each side of the equals sign.

`5x = -5`

Finally, to cancel down the answer, divide both sides of the equals sign by `5` because both sides are divisible by `5`.

`x = -1`