Answer
$\text{the interval }
\left( \dfrac{1}{8},2 \right)
$
Work Step by Step
Using compound inequalities, the solution to the given inequality, $
-3\lt4(2x-1)\lt12
,$ is
\begin{array}{l}\require{cancel}
-3\lt8x-4\lt12
\\\\
-3+4\lt8x-4+4\lt12+4
\\\\
1\lt8x\lt16
\\\\
\dfrac{1}{8}\lt\dfrac{8}{8}x\lt\dfrac{16}{8}
\\\\
\dfrac{1}{8}\lt x\lt2
.\end{array}
In interval notation, the solution is $
\text{the interval }
\left( \dfrac{1}{8},2 \right)
.$
