## Thomas' Calculus 13th Edition

$x\displaystyle \leq\frac{5}{4}$
Apply rules from the table "Rules for Inequalities" $5x- 3 \leq 7-3x\qquad$ ... add $3x+3\quad$ (rule 1) $5x+3x \leq 7+3$ $8x\leq 10\qquad$.... multiply with $c=\displaystyle \frac{1}{8}\quad$ (positive, rule 3) $x\displaystyle \leq\frac{10}{8}$ $x\displaystyle \leq\frac{5}{4}$ This inequality describes a closed interval, $x\displaystyle \in(-\infty,\frac{5}{4}]$ See table "Types of intervals."