Question

solve the following inequality for r. write your answer in simplest form.\\(-2r - 5(-5r + 9) \leq 6r + 9 + 7\\)

Explanation:

Step1: Expand left-hand side

$-2r + 25r - 45 \leq 6r + 9 + 7$

Step2: Simplify both sides

$23r - 45 \leq 6r + 16$

Step3: Isolate r terms (subtract 6r)

$23r - 6r - 45 \leq 16$
$17r - 45 \leq 16$

Step4: Isolate constant terms (add 45)

$17r \leq 16 + 45$
$17r \leq 61$

Step5: Solve for r (divide by 17)

$r \leq \frac{61}{17}$

Answer:

$r \leq \frac{61}{17}$