solve the inequality. 2(4x - 3) ≥ -3(3x) + 5x? x ≥ 0.5 x ≥ 2 (-∞, 0.5 (-∞, 2

Explanation:

Step1: Expand both sides

Expand $2(4x - 3)$ to get $8x-6$, and expand $-3(3x)+5x$ to get $-9x + 5x=-4x$. So the inequality becomes $8x-6\geq - 4x$.

Step2: Add $4x$ to both sides

$8x+4x-6\geq - 4x+4x$, which simplifies to $12x-6\geq0$.

Step3: Add 6 to both sides

$12x-6 + 6\geq0 + 6$, resulting in $12x\geq6$.

Step4: Divide both sides by 12

$\frac{12x}{12}\geq\frac{6}{12}$, so $x\geq0.5$.

Answer:

$x\geq0.5$