## Algebra 1: Common Core (15th Edition)

a. $a\geq-4$ b. $n\lt3$ c. $x\lt25$
a. $-6a-7\leq17$ Add 7 to both sides: $-6a-7+7\leq17+7$ Simplify: $-6a\leq24$ Divide both sides by $-6$: $\frac{-6a}{-6}\leq\frac{24}{-6}$ $a\geq-4$ (reverse the sign) Let's check: let a=2 $-6(2)-7\leq17$ $-12-7\leq17$ $-19\leq17$ This statement is true b. $-4\lt5-3n$ Switch sides: $5-3n\gt-4$ Subtract 5 from both sides: $5-3n-5\gt-4-5$ Simplify: $-3n\gt-9$ Divide both sides by $-3$: $\frac{-3n}{-3}\gt\frac{-9}{-3}$ (reverse the sign) $n\lt3$ Let's check: let n=-3 $-4\lt5-3(-3)$ $-4\lt14$ This statement is true c. $50\gt0.8x+30$ $50-30\gt0.8x+30-30$ $20\gt0.8x$ $\frac{20}{0.8}\gt\frac{0.8x}{0.8}$ $25\gt x$ Let's check: let x=10 $−6(10)−7\le 17$ $-67\leq17$ Statement is true