Question

solve for r.
-20r - 12 - 3 ≤ 9(-2r - 1)
write your answer with r first, followed by an inequality symbol.

Explanation:

Step1: Simplify left - hand side

Combine like terms on the left - hand side of the inequality: $-20r-12 - 3=-20r - 15$. So the inequality becomes $-20r-15\leq9(-2r - 1)$.

Step2: Expand right - hand side

Use the distributive property $a(b + c)=ab+ac$ on the right - hand side: $9(-2r - 1)=-18r-9$. Now the inequality is $-20r-15\leq - 18r-9$.

Step3: Add $20r$ to both sides

To get the $r$ terms on one side, add $20r$ to both sides: $-20r + 20r-15\leq-18r + 20r-9$, which simplifies to $-15\leq2r-9$.

Step4: Add 9 to both sides

Add 9 to both sides to isolate the term with $r$: $-15 + 9\leq2r-9 + 9$, resulting in $-6\leq2r$.

Step5: Divide both sides by 2

Divide both sides by 2 to solve for $r$: $\frac{-6}{2}\leq\frac{2r}{2}$, so $-3\leq r$.

Answer:

$r\geq - 3$