Question

solve the inequality.
$12 \left(\frac{1}{2}x - \frac{1}{3}\
ight) > 8 - 2x$
\\(\bigcirc\\) a. \\(x > -\frac{1}{2}\\)
\\(\bigcirc\\) b. \\(x > \frac{3}{2}\\)
\\(\bigcirc\\) c. \\(x > \frac{1}{2}\\)
\\(\bigcirc\\) d. \\(x > 3\\)

Explanation:

Step1: Distribute 12

Multiply 12 into the parentheses: \(12\times\frac{1}{2}x - 12\times\frac{1}{3} > 8 - 2x\)
Simplify: \(6x - 4 > 8 - 2x\)

Step2: Add 2x to both sides

To get all x terms on one side: \(6x + 2x - 4 > 8\)
Simplify: \(8x - 4 > 8\)

Step3: Add 4 to both sides

To isolate the term with x: \(8x > 8 + 4\)
Simplify: \(8x > 12\)

Step4: Divide by 8

Solve for x: \(x > \frac{12}{8}\)
Simplify the fraction: \(x > \frac{3}{2}\)

Answer:

B. \(x > \frac{3}{2}\)