#### Answer

$\left( \dfrac{1}{3},\dfrac{7}{3} \right)$

#### Work Step by Step

The given inequality, $
|-3x+4|-4\lt-1
,$ is equivalent to
\begin{array}{l}\require{cancel}
|-3x+4|\lt-1+4
\\\\
|-3x+4|\lt3
.\end{array}
Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-3\lt -3x+4\lt3
.\end{array}
Using the properties of inequality, then
\begin{array}{l}\require{cancel}
-3-4\lt -3x+4-4\lt3-4
\\\\
-7\lt -3x\lt-1
\\\\
\dfrac{-7}{-3}\gt \dfrac{-3x}{-3}\gt\dfrac{-1}{-3}
\\\\
\dfrac{7}{3}\gt x\gt\dfrac{1}{3}
\\\\
\dfrac{1}{3}\lt x\lt\dfrac{7}{3}
.\end{array}
Hence, the solution is the interval $
\left( \dfrac{1}{3},\dfrac{7}{3} \right)
.$