Question

How do you solve `-27x - 67= 122- 24x`?

Answer 1

`x = -63`

Explanation:

`-27x - 67 = 122 - 24x`

First, you want to remove the variable of the lowest value so that way you can solve this as a two-step equation. In this case, the variable with the lowest value is `-27x`. In order to get rid of it, we'll add `27x` to cancel out the `-27`. Because you add to one side, you must add to the other side to become equal. So, `27x - 24x = 3x` on the right side. Your equation should now look like this:

`-67 = 122 + 3x`

Now, subtract `122` from both sides to cancel out `122` in order to isolate for `x`. `-67 - 122 = -189`. Recall that two numbers of the same sign technically add up. Your equation should now look like this:

`-189 = 3x`

Now, divide by `3` in order to isolate for `x`. `3/3` = `1`, and `-189/3` = `-63`, so this will be the value of your variable.

`x = -63`

To verify that `x` really is `-63`, we'll plug it back into the equation. Replace `x` with the value `-63`.

`-27x - 67 = 122 - 24x`
`-27(-63) - 67 = 122 -24(-63)`
`1701 - 67 = 122 + 1512`
`1634 = 1634`

`x = -63`