Question

Solve each equation. Check your solution.

$\frac{1}{12}+\frac{3}{8}y=\frac{5}{12}+\frac{5}{8}y$

Short answer

The solution of the given equation is $y=-\frac{4}{3}$.

Step-by-step solution

Step 1. Write the given equation.

The given equation is “$\frac{1}{12}+\frac{3}{8}y=\frac{5}{12}+\frac{5}{8}y$”.

Step 2. Solve the given equation.

Solving,

$\frac{1}{12}+\frac{3}{8}y=\frac{5}{12}+\frac{5}{8}y$ (Given equation)

$\frac{1}{12}+\frac{3}{8}y-\frac{3}{8}y=\frac{5}{12}+\frac{5}{8}y-\frac{3}{8}y$ (Subtract $\frac{3}{8}y$from both sides)

$\frac{1}{12}=\frac{5}{12}+\frac{1}{4}y$ (Simplify)

$\frac{1}{12}-\frac{5}{12}=\frac{5}{12}+\frac{1}{4}y-\frac{5}{12}$ (Subtract $\frac{5}{12}$from both sides)

$-\frac{1}{3}=\frac{1}{4}y$ (Simplify)

$-\frac{1}{3}\times 4=\frac{1}{4}y\times 4$ (Multiply both sides by 4)

$-\frac{4}{3}=y$ (Simplify)

$y=-\frac{4}{3}$ (Write the variable on the left-hand side)

So, $y=-\frac{4}{3}$is the solution of the given equation.

Step 3. Check the obtained solution.

Put $y=-\frac{4}{3}$in the given equation $\frac{1}{12}+\frac{3}{8}y=\frac{5}{12}+\frac{5}{8}y$to get,

$\begin{array}{l}\frac{1}{12}+\frac{3}{8}\left(-\frac{4}{3}\right)=\frac{5}{12}+\frac{5}{8}\left(-\frac{4}{3}\right)\\ \frac{1}{12}-\frac{1}{2}=\frac{5}{12}-\frac{5}{6}\\ \frac{1-6}{12}=\frac{5-10}{12}\\ -\frac{5}{12}=-\frac{5}{12}\end{array}$

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.