Answer
$x=\left\{ -\dfrac{14}{3}, \dfrac{16}{3} \right\}$
Work Step by Step
Using the properties of equality, the given equation, $
|3x-1|+10=25
,$ is equivalent to
\begin{array}{l}\require{cancel}
|3x-1|+10-10=25-10
\\
|3x-1|=15
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above implies
\begin{array}{l}\require{cancel}
3x-1=15
\\\\\text{OR}\\\\
3x-1=-15
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
3x-1=15
\\
3x-1+1=15+1
\\
3x=16
\\
\dfrac{3x}{3}=\dfrac{16}{3}
\\
x=\dfrac{16}{3}
\\\\\text{OR}\\\\
3x-1=-15
\\
3x-1+1=-15+1
\\
3x=-14
\\
\dfrac{3x}{3}=-\dfrac{14}{3}
\\
x=-\dfrac{14}{3}
.\end{array}
Hence, the solutions are $
x=\left\{ -\dfrac{14}{3}, \dfrac{16}{3} \right\}
.$
