Answer
$x=\left\{ -\dfrac{1}{3},3 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
5-2|3x-4|=-5
,$ 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}
5-2|3x-4|=-5
\\\\
-2|3x-4|=-5-5
\\\\
-2|3x-4|=-10
\\\\
|3x-4|=\dfrac{-10}{-2}
\\\\
|3x-4|=5
.\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}
3x-4=5
\\\\\text{OR}\\\\
3x-4=-5
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x-4=5
\\\\
3x=5+4
\\\\
3x=9
\\\\
x=\dfrac{9}{3}
\\\\
x=3
\\\\\text{OR}\\\\
3x-4=-5
\\\\
3x=-5+4
\\\\
3x=-1
\\\\
x=-\dfrac{1}{3}
.\end{array}
Hence, $
x=\left\{ -\dfrac{1}{3},3 \right\}
.$