Answer
$
\left( -3,4 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|2x-1| \lt 7
,$ use the definition of absolute value inequalities. Use the properties of inequalities to isolate the variable.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-7 \lt 2x-1 \lt 7
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-7+1 \lt 2x-1+1 \lt 7+1
\\\\
-6 \lt 2x \lt 8
\\\\
-\dfrac{6}{2} \lt \dfrac{2x}{2} \lt \dfrac{8}{2}
\\\\
-3 \lt x \lt 4
.\end{array}
In interval notation, the solution set is $
\left( -3,4 \right)
.$
The colored graph is the graph of the solution set.