## Intermediate Algebra (12th Edition)

$\left( -\infty,\infty \right)$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $7(4-x)+5x\lt2(16-x) ,$ use the Distributive Property and the properties of inequality. 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 Distributive Property and the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} 7(4)+7(-x)+5x\lt2(16)+2(-x) \\\\ 28-7x+5x\lt32-2x \\\\ -7x+5x+2x\lt32-28 \\\\ 0\lt4 \text{ (TRUE)} .\end{array} Since the solution above ended with a TRUE statement, then the solution set is the set of all real numbers. In interval notation, the solution set is $\left( -\infty,\infty \right) .$ The graph of the solution set is the number line itself.