Question

8(5 - 2y) ≥ 15 - 9(2y + 3)

Explanation:

Step1: Expand both sides

Left side: \(8(5 - 2y)=40 - 16y\)
Right side: \(15-9(2y + 3)=15-(18y + 27)=15 - 18y - 27=-12 - 18y\)
So the inequality becomes \(40 - 16y\geq - 12 - 18y\)

Step2: Move terms with \(y\) to one side

Add \(18y\) to both sides: \(40 - 16y+18y\geq - 12 - 18y+18y\)
Simplify: \(40 + 2y\geq - 12\)

Step3: Isolate \(y\)

Subtract 40 from both sides: \(40 + 2y-40\geq - 12-40\)
Simplify: \(2y\geq - 52\)

Step4: Solve for \(y\)

Divide both sides by 2: \(\frac{2y}{2}\geq\frac{-52}{2}\)
Simplify: \(y\geq - 26\)

Answer:

\(y\geq - 26\)