Answer
$w=-1\text{ OR }w=\dfrac{3}{2}$
Work Step by Step
Using the properties of equality, the given equation, $
3|4w-1|-5=10
,$ is equivalent to
\begin{array}{l}\require{cancel}
3|4w-1|-5+5=10+5
\\
3|4w-1|=15
\\
\dfrac{3|4w-1|}{3}=\dfrac{15}{3}
\\
|4w-1|=5
.\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}
4w-1=5
\\\\\text{OR}\\\\
4w-1=-5
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
4w-1=5
\\
4w-1+1=5+1
\\
4w=6
\\
\dfrac{4w}{4}=\dfrac{6}{4}
\\
w=\dfrac{3}{2}
\\\\\text{OR}\\\\
4w-1=-5
\\
4w-1+1=-5+1
\\
4w=-4
\\
\dfrac{4w}{4}=-\dfrac{4}{4}
\\
w=-1
.\end{array}
Hence, $
w=-1\text{ OR }w=\dfrac{3}{2}
.$
