Question

what is the value of x in the equation $\frac{2}{3}(\frac{1}{2}x + 12) = \frac{1}{2}(\frac{1}{3}x + 14) - 3?$○ $-24$○ $-6$○ $-\frac{2}{3}$○ $0$

Explanation:

Step1: Expand both sides

$\frac{2}{3} \times \frac{1}{2}x + \frac{2}{3} \times 12 = \frac{1}{2} \times \frac{1}{3}x + \frac{1}{2} \times 14 - 3$
Simplify to: $\frac{1}{3}x + 8 = \frac{1}{6}x + 7 - 3$

Step2: Simplify right-hand side

$\frac{1}{3}x + 8 = \frac{1}{6}x + 4$

Step3: Subtract $\frac{1}{6}x$ from both sides

$\frac{1}{3}x - \frac{1}{6}x + 8 = 4$
Simplify to: $\frac{1}{6}x + 8 = 4$

Step4: Subtract 8 from both sides

$\frac{1}{6}x = 4 - 8$
Simplify to: $\frac{1}{6}x = -4$

Step5: Solve for x

$x = -4 \times 6$

Answer:

-24