## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$x\gt-\dfrac{2}{17}$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $2(4+2x)\gt2x+3(2-5x) ,$ use the Distributive Property and the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to \begin{array}{l}\require{cancel} 2(4+2x)\gt2x+3(2-5x) \\\\ 2(4)+2(2x)\gt2x+3(2)+3(-5x) \\\\ 8+4x\gt2x+6-15x .\end{array} Using the properties of inequality to isolate the variable, then \begin{array}{l}\require{cancel} 8+4x\gt2x+6-15x \\\\ 4x-2x+15x\gt6-8 \\\\ 17x\gt-2 \\\\ x\gt-\dfrac{2}{17} .\end{array}