# How do you solve |5x-4| +3 = 3?

Apr 29, 2017

See the solution process below:

#### Explanation:

First, subtract $\textcolor{red}{3}$ from each side of the equation to isolate the absolute value function while keeping the equation balanced:

$\left\mid 5 x - 4 \right\mid + 3 - \textcolor{red}{3} = 3 - \textcolor{red}{3}$

$\left\mid 5 x - 4 \right\mid + 0 = 0$

$\left\mid 5 x - 4 \right\mid = 0$

Normally an absolute value equality would produce two answers. However, because the absolute value function is equal to $0$ there is only one solution.

We can equate the term within the absolute value to $0$ and solve for $x$:

$5 x - 4 = 0$

$5 x - 4 + \textcolor{red}{4} = 0 + \textcolor{red}{4}$

$5 x - 0 = 4$

$5 x = 4$

$\frac{5 x}{\textcolor{red}{5}} = \frac{4}{\textcolor{red}{5}}$

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

$x = \frac{4}{5}$