## Intermediate Algebra (12th Edition)

$\left( -3,4 \right)$
$\bf{\text{Solution Outline:}}$ 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.