Answer
$x=\left\{ \dfrac{3}{2},\dfrac{7}{2} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
3|2x-5|-7=-1
,$ isolate first the absolute value expression. Then use the definition of an absolute value equality. Finally, use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the proeprties of equality to isolate the absolute value expression, the given is equivalent to
\begin{array}{l}\require{cancel}
3|2x-5|-7=-1
\\\\
3|2x-5|=-1+7
\\\\
3|2x-5|=6
\\\\
|2x-5|=\dfrac{6}{3}
\\\\
|2x-5|=2
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
2x-5=2
\\\\\text{OR}\\\\
2x-5=-2
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x-5=2
\\\\
2x=2+5
\\\\
2x=7
\\\\
x=\dfrac{7}{2}
\\\\\text{OR}\\\\
2x-5=-2
\\\\
2x=-2+5
\\\\
2x=3
\\\\
x=\dfrac{3}{2}
.\end{array}
Hence, $
x=\left\{ \dfrac{3}{2},\dfrac{7}{2} \right\}
.$
