Question

solve the inequality for x.
5(3x + 5) ≥ 9x + 7
simplify your answer as much as possible.

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(5(3x + 5)\) to get \(15x+25\). So the inequality becomes \(15x + 25\geq9x+7\).

Step2: Subtract \(9x\) from both sides

Subtracting \(9x\) from both sides gives \(15x-9x + 25\geq9x-9x+7\), which simplifies to \(6x+25\geq7\).

Step3: Subtract 25 from both sides

Subtracting 25 from both sides: \(6x+25 - 25\geq7 - 25\), so \(6x\geq - 18\).

Step4: Divide both sides by 6

Dividing both sides by 6 (since 6 is positive, the inequality sign remains the same): \(\frac{6x}{6}\geq\frac{-18}{6}\), which simplifies to \(x\geq - 3\).

Answer:

\(x\geq - 3\)