# How do you solve abs(5x + 10) - 15 = 20?

Aug 2, 2015

$x = - 9 , 5$

#### Explanation:

Rearrange the equation:
$| 5 x + 10 | - 15 = 20$

=>

$| 5 x + 10 | = 35$

Because of the modulus there are two solutions, the first:

$5 x + 10 = 35$ => $x = 5$

The second:

$5 x + 10 = - 35$ => $x = - 9$

Aug 2, 2015

$x = - 9 , 5$

#### Explanation:

$\left\mid 5 x + 10 \right\mid - 15 = 20$

Add $15$ to both sides of the equation.

$\left\mid 5 x + 10 \right\mid = 20 + 15$ =

$\left\mid 5 x + 10 \right\mid = 35$

Rewrite the equation without the absolute value symbol, with one equation positive, and one negative.

$5 x + 10 = 35$ and

$- \left(5 x + 10\right) = 35$.

Positive Equation

$5 x + 10 = 35$

Subtract $10$ from both sides of the equation.

$5 x = 35 - 10$ =

$5 x = 25$

Divide both sides by $5$.

$x = \frac{25}{5}$ =

$x = 5$

Negative Equation

$- \left(5 x + 10\right) = 35$ =

$- 5 x - 10 = 35$

Add $10$ to both sides.

$- 5 x = 35 + 10$ =

$- 5 x = 45$

Divide both sides by $- 5$.

$x = \frac{45}{- 5}$ =

$x = - 9$