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

Jul 15, 2015

$w = - 4$

#### Explanation:

$\left\mid 4 w - 1 \right\mid = 5 w + 37$

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

$4 w - 1 = 5 w + 37$ and $- \left(4 w - 1\right) = 5 w + 37$

Positive equation

$4 w - 1 = 5 w + 37$

Add $1$ to both sides.

$4 w = 5 w + 38$

Subtract $5 w$ from both sides.

$4 w - 5 w = 38$

$- w = 38$

Multiply both sides times $- 1$.

$w = - 38$

Check.

$\left\mid 4 \cdot - 38 - 1 \right\mid = 5 \cdot - 38 + 37$ =

$\left\mid - 152 \right\mid \ne - 153$

$152 \ne - 153$

$w \ne - 38$

Negative equation

$- \left(4 w - 1\right) = 5 w + 37$ =

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

Subtract $1$ from both sides.

$- 4 w = 5 w + 36$

Subtract $5 w$ from both sides

$- 4 w - 5 w = 36$

$- 9 w = 36$

Divide both sides by $- 9$.

$w = \frac{36}{- 9} = - 4$

$w = - 4$

Check.

$\left\mid 4 \cdot - 4 - 1 \right\mid = 5 \cdot - 4 + 37$ =

$\left\mid - 17 \right\mid = - 20 + 37$ =

$17 = 17$

$w = - 4$ checks.