Question

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

Explanation:

Step1: Expand left side

$9r + 20r + 20 \leq -9r + 15$

Step2: Combine like terms left

$29r + 20 \leq -9r + 15$

Step3: Add $9r$ to both sides

$38r + 20 \leq 15$

Step4: Subtract 20 from both sides

$38r \leq -5$

Step5: Divide by 38

$r \leq -\frac{5}{38}$

Wait, correction in Step1: $-4(-5r -5) = 20r +20$, right side $10+5=15$. Step2: $9r+20r=29r$, so $29r+20 \leq -9r+15$. Step3: $29r+9r=38r$, so $38r+20 \leq15$. Step4: $38r \leq15-20=-5$. Step5: $r \leq -5/38$. Yes, that's correct.

Final Answer: $r \leq -\frac{5}{38}$

Step1: Expand left term

$9r + 20r + 20 \leq -9r + 15$

Step2: Combine left like terms

$29r + 20 \leq -9r + 15$

Step3: Add $9r$ to both sides

$38r + 20 \leq 15$

Step4: Subtract 20 from both sides

$38r \leq -5$

Step5: Divide by 38

$r \leq -\frac{5}{38}$

Answer:

$r \leq -\frac{5}{33}$