## Intermediate Algebra (12th Edition)

$x\gt-\dfrac{1}{2}$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $3-2(x+3)\lt4x ,$ use first the Distributive Property. 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 expression above is equivalent to \begin{array}{l}\require{cancel} 3-2(x)-2(3)\lt4x \\\\ 3-2x-6\lt4x .\end{array} Using the properties of inequality to combine like terms, the inequality above is equivalent to \begin{array}{l}\require{cancel} -2x-4x\lt-3+6 \\\\ -6x\lt3 .\end{array} Dividing both sides by $-6 ,$ in which the inequality symbol reverses, results to \begin{array}{l}\require{cancel} x\gt\dfrac{3}{-6} \\\\ x\gt-\dfrac{1}{2} .\end{array}