Q32. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{1}{8}\left(3d-2\right)=\frac{1}{4}\left(d+5\right)$

Step-by-Step Solution

Answer

The solution of the given equation is $d=12$.

Step 1. Write the given equation.

The given equation is “$\frac{1}{8}\left(3d-2\right)=\frac{1}{4}\left(d+5\right)$”.

Step 2. Solve the given equation.

Solving,

$\frac{1}{8}\left(3d-2\right)=\frac{1}{4}\left(d+5\right)$  (Given equation)

$\frac{1}{8}\left(3d-2\right)\times 8=\frac{1}{4}\left(d+5\right)\times 8$  (Multiply both sides by 8)

$3d-2=2\left(d+5\right)$  (Simplify)

$3d-2=2d+10$  (Distributive property)

$3d-2-2d=2d+10-2d$  (Subtract $2d$ from both sides)

$d-2=10$  (Simplify)

$d-2+2=10+2$  (Add 2 to both sides)

$d=12$  (Simplify)

So, $d=12$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $d=12$ in the given equation $\frac{1}{8}\left(3d-2\right)=\frac{1}{4}\left(d+5\right)$ to get,

$\begin{array}{l}\frac{1}{8}\left(3\left(12\right)-2\right)=\frac{1}{4}\left(12+5\right)\\ \frac{1}{8}\left(36-2\right)=\frac{1}{4}\left(17\right)\\ \frac{1}{8}\left(34\right)=\frac{17}{4}\\ \frac{17}{4}=\frac{17}{4}\end{array}$

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.