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

$x\gt\dfrac{16}{5}$
$\bf{\text{Solution Outline:}}$ Use the Distributive Property and the properties of inequality to solve the given, $3(7-x)\lt2x+5 .$ $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 3(7-x)\lt2x+5 \\\\ 3(7)+3(-x)\lt2x+5 \\\\ 21-3x\lt2x+5 .\end{array} Using the properties of equality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 21-3x\lt2x+5 \\\\ -3x-2x\lt5-21 \\\\ -5x\lt-16 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to \begin{array}{l}\require{cancel} -5x\lt-16 \\\\ x\gt\dfrac{-16}{-5} \\\\ x\gt\dfrac{16}{5} .\end{array}