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

$x\lt\dfrac{13}{2}$
$\bf{\text{Solution Outline:}}$ Use the Distributive Property to simplify the given inequality, $9(x-3)-4x\lt2-(3-x) .$ Then use 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} 9(x-3)-4x\lt2-(3-x) \\\\ 9(x)+9(-3)-4x\lt2-1(3)-1(-x) \\\\ 9x-27-4x\lt2-3+x .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 9x-27-4x\lt2-3+x \\\\ 9x-4x-x\lt2-3+27 \\\\ 4x\lt26 \\\\ x\lt\dfrac{26}{4} \\\\ x\lt\dfrac{13}{2} .\end{array}