Question

solve the equation: 2/3(3x + 1/2) - 1/4 = 1/3

Explanation:

Step1: Add 1/4 to both sides

$\frac{2}{3}(3x + \frac{1}{2}) = \frac{1}{3} + \frac{1}{4}$
Find a common denominator for the right side, which is 12. So $\frac{1}{3}=\frac{4}{12}$ and $\frac{1}{4}=\frac{3}{12}$. Then $\frac{4}{12}+\frac{3}{12}=\frac{7}{12}$. So the equation becomes $\frac{2}{3}(3x + \frac{1}{2}) = \frac{7}{12}$.

Step2: Multiply both sides by 3/2

$3x + \frac{1}{2} = \frac{7}{12} \times \frac{3}{2}$
Simplify the right side: $\frac{7}{12} \times \frac{3}{2}=\frac{7\times3}{12\times2}=\frac{21}{24}=\frac{7}{8}$. So now we have $3x + \frac{1}{2} = \frac{7}{8}$.

Step3: Subtract 1/2 from both sides

$3x = \frac{7}{8} - \frac{1}{2}$
Find a common denominator for the right side, which is 8. $\frac{1}{2}=\frac{4}{8}$. So $\frac{7}{8}-\frac{4}{8}=\frac{3}{8}$. Now the equation is $3x = \frac{3}{8}$.

Step4: Divide both sides by 3

$x = \frac{3}{8} \div 3$
Dividing by 3 is the same as multiplying by 1/3, so $x = \frac{3}{8} \times \frac{1}{3}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$