Question

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

Explanation:

Step1: Expand both sides

First, expand the left - hand side and the right - hand side of the inequality.
The left - hand side: \(2(4x - 3)=2\times4x-2\times3 = 8x-6\)
The right - hand side: \(-3(3x)+5x=-9x + 5x=-4x\)
So the inequality becomes \(8x-6\geq - 4x\)

Step2: Move all x terms to one side

Add \(4x\) to both sides of the inequality to get all the \(x\) terms on the left - hand side.
\(8x + 4x-6\geq-4x + 4x\)
\(12x-6\geq0\)

Step3: Isolate the x term

Add 6 to both sides of the inequality:
\(12x-6 + 6\geq0 + 6\)
\(12x\geq6\)

Step4: Solve for x

Divide both sides of the inequality by 12:
\(x\geq\frac{6}{12}\)
Simplify \(\frac{6}{12}\) to get \(x\geq0.5\)

Answer:

\(x\geq0.5\) (or in the option format: A. \(x\geq0.5\))