# How do you solve abs(-4+5x)=16?

Apr 19, 2018

$x = - \frac{12}{5} , 4$

#### Explanation:

Solve:

$\left\mid - 4 + 5 x \right\mid = 16$

Since $\left\mid a \right\mid = + a \mathmr{and} - a$, the equation can be broken into positive and a negative equations.

$- 4 + 5 x = 16$

and

$- \left(- 4 + 5 x\right) = 16$

Positive Equation

$- 4 + 5 x = 16$

Add $4$ to both sides.

$- \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} + 5 x = 16 + 4$

Simplify.

$5 x = 20$

Divide both sides by $5$.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} = \frac{20}{5}$

Simplify.

$x = 4$

Negative Equation

$- \left(- 4 + 5 x\right) = 16$

Distribute the $- 1$ on the left-hand side.

$4 - 5 x = 16$

Subtract $4$ from both sides.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} - 5 x = 16 - 4$

Simplify.

$- 5 x = 12$

Divide both sides by $- 5$.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5}}} x} = \frac{12}{- 5}$

$x = - \frac{12}{5}$

Collect all solutions.

$x = - \frac{12}{5} , 4$