Intermediate Algebra (12th Edition)

$\left( 1,2 \right)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $-1 \lt 3x-4 \lt 2 ,$ use the properties of inequality 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 $\ge.$ $\bf{\text{Solution Details:}}$ Using the properties of inequality to isolate the variable results to \begin{array}{l}\require{cancel} -1+4 \lt 3x-4+4 \lt 2+4 \\\\ 3 \lt 3x \lt 6 \\\\ \dfrac{3}{3} \lt \dfrac{3x}{3} \lt \dfrac{6}{3} \\\\ 1 \lt x \lt 2 .\end{array} In interval notation, the solution set is $\left( 1,2 \right) .$ The colored graph is the graph of the solution set.