Answer
$x=\left\{ -\dfrac{16}{5},2 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|5x+3|-10=3
,$ use the properties of equality to isolate the absolute value expression. Then use the definition of absolute value to solve for the value/s of the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
|5x+3|=3+10
\\\\
|5x+3|=13
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
5x+3=13
\\\\\text{OR}\\\\
5x+3=-13
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
5x+3=13
\\\\
5x=13-3
\\\\
5x=10
\\\\
x=\dfrac{10}{5}
\\\\
x=2
\\\\\text{OR}\\\\
5x+3=-13
\\\\
5x=-13-3
\\\\
5x=-16
\\\\
x=-\dfrac{16}{5}
.\end{array}
Hence, $
x=\left\{ -\dfrac{16}{5},2 \right\}
.$
