Answer
a. $a\geq-4$
b. $n\lt3$
c. $x\lt25$
Work Step by Step
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
