Question

Solve the equation by first clearing the fractions.

$-\frac{1}{12}=\frac{1}{2}x-\frac{4}{9}$

Short answer

The solution is $x=\frac{13}{18}$.

Step-by-step solution

Step 1. Given Information.

The equation is $-\frac{1}{12}=\frac{1}{2}x-\frac{4}{9}$.

Step 2. Calculation.

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

$\begin{array}{c}-\frac{1}{12}=\frac{1}{2}x-\frac{4}{9}\\ 36\left(-\frac{1}{12}\right)=36\left(\frac{1}{2}x-\frac{4}{9}\right)\\ 36\left(-\frac{1}{12}\right)=36\left(\frac{1}{2}x\right)-36\left(\frac{4}{9}\right)\\ -3=18x-16\end{array}$

On further simplification,

$\begin{array}{c}18x=-3+16\\ 18x=13\\ x=\frac{13}{18}\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=\frac{13}{18}$.