Question

solve the equation: 3/4x + 1/2 = 5/8

Explanation:

Step1: Subtract $\frac{1}{2}$ from both sides

We start with the equation $\frac{3}{4}x+\frac{1}{2}=\frac{5}{8}$. Subtract $\frac{1}{2}$ from both sides to isolate the term with $x$. First, convert $\frac{1}{2}$ to eighths: $\frac{1}{2}=\frac{4}{8}$. So the equation becomes $\frac{3}{4}x+\frac{4}{8}=\frac{5}{8}$. Subtracting $\frac{4}{8}$ from both sides gives $\frac{3}{4}x=\frac{5}{8}-\frac{4}{8}=\frac{1}{8}$.

Step2: Solve for $x$

Now we have $\frac{3}{4}x = \frac{1}{8}$. To solve for $x$, we multiply both sides by the reciprocal of $\frac{3}{4}$, which is $\frac{4}{3}$. So $x=\frac{1}{8}\times\frac{4}{3}$. Simplifying the right side, we get $x = \frac{4}{24}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$