Answer
$x=\left\{ -\dfrac{5}{3},\dfrac{11}{3} \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|3(x-1)|=8
,$ use the Distributive Property and the definition of absolute value equality. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Distributive Property, the given equation is equivalent to
\begin{array}{l}\require{cancel}
|3(x)+3(-1)|=8
\\\\
|3x-3|=8
.\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}
3x-3=8
\\\\\text{OR}\\\\
3x-3=-8
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x-3=8
\\\\
3x=8+3
\\\\
3x=11
\\\\
x=\dfrac{11}{3}
\\\\\text{OR}\\\\
3x-3=-8
\\\\
3x=-8+3
\\\\
3x=-5
\\\\
x=-\dfrac{5}{3}
.\end{array}
Hence, $
x=\left\{ -\dfrac{5}{3},\dfrac{11}{3} \right\}
.$
