Answer
$x=\left\{ -\dfrac{7}{2},\dfrac{9}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|2x-1|=8
,$ use the definition of absolute value equality. Then use the properties of equality to isolate the variable in each resulting equation.
$\bf{\text{Solution Details:}}$
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}
2x-1=8
\\\\\text{OR}\\\\
2x-1=-8
.\end{array}
Using the properties of equality to isolate the variable in each equation results to
\begin{array}{l}\require{cancel}
2x-1=8
\\\\
2x=8+1
\\\\
2x=9
\\\\
x=\dfrac{9}{2}
\\\\\text{OR}\\\\
2x-1=-8
\\\\
2x=-8+1
\\\\
2x=-7
\\\\
x=-\dfrac{7}{2}
.\end{array}
Hence, $
x=\left\{ -\dfrac{7}{2},\dfrac{9}{2} \right\}
.$
