Question

linear inequalities (level 2)
question
solve the following inequality for r. write your answer in simplest form.
-2r - 5(-5r + 9) ≤ 6r + 9 + 7

Explanation:

Step1: Distribute the -5

First, we distribute the -5 in the term \(-5(-5r + 9)\). Using the distributive property \(a(b + c)=ab+ac\), we get:
\(-2r + 25r-45\leq6r + 9 + 7\)

Step2: Combine like terms on left and right

On the left side, combine \(-2r\) and \(25r\):
\(23r-45\leq6r + 16\)

Step3: Subtract 6r from both sides

Subtract \(6r\) from both sides to get all the \(r\) terms on the left:
\(23r-6r - 45\leq16\)
\(17r-45\leq16\)

Step4: Add 45 to both sides

Add 45 to both sides to isolate the term with \(r\):
\(17r\leq16 + 45\)
\(17r\leq61\)

Step5: Divide both sides by 17

Divide both sides by 17 to solve for \(r\):
\(r\leq\frac{61}{17}\)

Answer:

\(r\leq\frac{61}{17}\)