Question

which is the solution to the inequality?
$2x - 3 \geq -4x + 2$
a. $x \geq \frac{1}{2}$
b. $x \leq \frac{1}{2}$
c. $x \geq \frac{5}{6}$
d. $x \leq \frac{5}{6}$

Explanation:

Step1: Add \(4x\) to both sides

To isolate the \(x\) terms on one side, we add \(4x\) to both sides of the inequality \(2x - 3\geq - 4x+2\). This gives us \(2x + 4x-3\geq - 4x + 4x+2\), which simplifies to \(6x-3\geq2\).

Step2: Add 3 to both sides

Next, we add 3 to both sides of the inequality \(6x - 3\geq2\) to isolate the term with \(x\). This results in \(6x-3 + 3\geq2 + 3\), which simplifies to \(6x\geq5\).

Step3: Divide both sides by 6

Finally, we divide both sides of the inequality \(6x\geq5\) by 6. Since 6 is a positive number, the direction of the inequality sign remains the same. So we get \(x\geq\frac{5}{6}\).

Answer:

C. \(x\geq\frac{5}{6}\)