solve the following inequality for r. write your answer in simplest form.\n-9 + 4(-2r - 10) ≥ 4r - 5 + 10r

Explanation:

Step1: Expand the left - hand side

$$ \begin{align*} -9+4(-2r - 10)&=-9-8r-40\ &=-8r - 49 \end{align*} $$

Step2: Simplify the right - hand side

$$ 4r-5 + 10r=14r-5 $$

Step3: Rewrite the inequality

The inequality becomes $-8r - 49\geq14r-5$

Step4: Move the terms with $r$ to one side

Add $8r$ to both sides: $-49\geq14r + 8r-5$, which simplifies to $-49\geq22r-5$

Step5: Move the constant term

Add $5$ to both sides: $-49 + 5\geq22r$, so $-44\geq22r$

Step6: Solve for $r$

Divide both sides by $22$: $r\leq - 2$

Answer:

$r\leq - 2$