Question

How do you solve `-2|-5x + 2| + 2 = -74`?

Answer 1

`x = -7.2, 8`

Explanation:

Start rearranging the bits outside of the modulus:

`-2|-5x+2|+2 = -74`
`|-5x+2| = (-76)/(-2)=38`

A modulus is a positive or negative become positive. There are two ways to solve it.

Firstly, you can square both sides, because either positive or negative numbers squared become positive. However, `38^2` is a big number, so this is considerably more difficult than the second method.

Solve two equations, a positive and a negative.

1) `-5x+2=38`
2) `-5x+2=-38`

Now solve each:

1) `-5x+2=38`
`-5x = 36`
`x = -7.2`

2) `-5x+2=-38`
`-5x = -40`
`x = 8`

So now you have your solutions:

`x = -7.2, +8`