Question

simplify the equation: 2/5(3x - 1/2) = 4/5

Explanation:

Step1: Eliminate fraction by multiplying both sides by 5/2

Multiply both sides of the equation $\frac{2}{5}(3x - \frac{1}{2}) = \frac{4}{5}$ by $\frac{5}{2}$ to get rid of the coefficient $\frac{2}{5}$ on the left side. So we have $3x - \frac{1}{2}=\frac{4}{5}\times\frac{5}{2}$.

Step2: Simplify the right side

Calculate $\frac{4}{5}\times\frac{5}{2}$, the 5s cancel out, and we get $\frac{4}{2} = 2$. So the equation becomes $3x - \frac{1}{2}=2$.

Step3: Add 1/2 to both sides

Add $\frac{1}{2}$ to both sides of the equation $3x - \frac{1}{2}=2$ to isolate the term with $x$. So $3x=2 + \frac{1}{2}$.

Step4: Simplify the right side

Convert 2 to $\frac{4}{2}$, then add $\frac{4}{2}+\frac{1}{2}=\frac{5}{2}$. So $3x=\frac{5}{2}$.

Step5: Divide both sides by 3

Divide both sides of the equation $3x=\frac{5}{2}$ by 3, which is the same as multiplying by $\frac{1}{3}$. So $x=\frac{5}{2}\times\frac{1}{3}=\frac{5}{6}$.

Answer:

$\frac{5}{6}$ (corresponding to the red option with 5/6)