Question

Solve the equation by first clearing the fractions.

$\frac{1}{2}x+\frac{3}{4}=\frac{5}{6}$

Short answer

The solution is $x=\frac{1}{6}$.

Step-by-step solution

Step 1. Given Information.

The equation is $\frac{1}{2}x+\frac{3}{4}=\frac{5}{6}$.

Step 2. Calculation.

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

$\begin{array}{c}\frac{1}{2}x+\frac{3}{4}=\frac{5}{6}\\ 12\left(\frac{1}{2}x+\frac{3}{4}\right)=12\left(\frac{5}{6}\right)\\ 12\left(\frac{1}{2}x\right)+12\left(\frac{3}{4}\right)=12\left(\frac{5}{6}\right)\\ 6x+9=10\end{array}$

On further simplification,

$\begin{array}{c}6x=10-9\\ 6x=1\\ x=\frac{1}{6}\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=\frac{1}{6}$.