Question

How do you solve `abs(4w - 1) = 5w + 37`?

Answer 1

`w=-4`

Explanation:

`abs(4w-1)=5w+37`

Separate the equation into a positive equation and a negative equation.

`4w-1=5w+37` and `-(4w-1)=5w+37`

Positive equation

`4w-1=5w+37`

Add `1` to both sides.

`4w=5w+38`

Subtract `5w` from both sides.

`4w-5w=38`

`-w=38`

Multiply both sides times `-1`.

`w=-38`

Check.

`abs(4*-38-1)=5*-38+37` =

`abs(-152)!=-153`

`152!=-153`

`w!=-38`

Negative equation

`-(4w-1)=5w+37` =

`-4w+1=5w+37`

Subtract `1` from both sides.

`-4w=5w+36`

Subtract `5w` from both sides

`-4w-5w=36`

`-9w=36`

Divide both sides by `-9`.

`w=36/(-9)=-4`

`w=-4`

Check.

`abs(4*-4-1)=5*-4+37` =

`abs(-17)=-20+37` =

`17=17`

`w=-4` checks.