Answer
$\text{the interval }
\left( -\dfrac{3}{5},0 \right)
$
Work Step by Step
Using compound inequalities, the solution to the given inequality, $
-6\lt x-(3-4x) \lt -3
,$ is
\begin{array}{l}\require{cancel}
-6\lt x-3+4x \lt -3
\\\\
-6\lt -3+5x \lt -3
\\\\
-6+3\lt -3+5x+3 \lt -3+3
\\\\
-3\lt 5x \lt 0
\\\\
-\dfrac{3}{5}\lt \dfrac{5}{5}x \lt \dfrac{0}{5}
\\\\
-\dfrac{3}{5}\lt x \lt 0
.\end{array}
In interval notation, the solution is $
\text{the interval }
\left( -\dfrac{3}{5},0 \right)
.$
