Question

Solve the equation by first clearing the fractions.

$\frac{7}{10}x-\frac{1}{5}=\frac{3}{8}$

Short answer

The solution is $x=\frac{23}{28}$.

Step-by-step solution

Step 1. Given Information.

The equation is$\frac{7}{10}x-\frac{1}{5}=\frac{3}{8}$.

Step 2. Calculation.

First, find out the LCD and then the LCD has to substitute each side.

$\begin{array}{c}\frac{7}{10}x-\frac{1}{5}=\frac{3}{8}\\ 40\left(\frac{7}{10}x-\frac{1}{5}\right)=40\left(\frac{3}{8}\right)\\ 40\left(\frac{7}{10}x\right)-40\left(\frac{1}{5}\right)=40\left(\frac{3}{8}\right)\\ 28x-8=15\end{array}$

On further simplification,

$\begin{array}{c}28x=15+8\\ 28x=23\\ x=\frac{23}{28}\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=\frac{23}{28}$.