Question

solve the inequality.
-2x ≤ \frac{-3(x + 1)}{2}
x ≥ ?

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the inequality \(-2x \leq \frac{-3(x + 1)}{2}\) by 2 to get rid of the fraction. We have \(2\times(-2x) \leq -3(x + 1)\), which simplifies to \(-4x \leq -3x - 3\).

Step2: Isolate the variable \(x\)

Add \(4x\) to both sides of the inequality: \(-4x + 4x \leq -3x - 3 + 4x\), which gives \(0 \leq x - 3\). Then add 3 to both sides: \(0 + 3 \leq x - 3 + 3\), so \(3 \leq x\), or \(x \geq 3\).

Answer:

\(3\)