Q31. - Algebra 1

Question

Solve each equation. Check your solution.

$\frac{2m}{5}=\frac{1}{3}\left(2m-12\right)$

Step-by-Step Solution

Answer

The solution of the given equation is $m=15$.

Step 1. Write the given equation.

The given equation is “$\frac{2m}{5}=\frac{1}{3}\left(2m-12\right)$”.

Step 2. Solve the given equation.

Solving,

$\frac{2m}{5}=\frac{1}{3}\left(2m-12\right)$  (Given equation)

$6m=5\left(2m-12\right)$  (Cross-multiply)

$6m=10m-60$  (Distributive property)

$6m-10m=10m-60-10m$  (Subtract $10m$ from both sides)

$-4m=-60$  (Simplify)

$\frac{-4m}{-4}=\frac{-60}{-4}$  (Divide both sides by $-4$)

$m=15$  (Simplify)

So, $m=15$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $m=15$ in the given equation $\frac{2m}{5}=\frac{1}{3}\left(2m-12\right)$ to get,

$\begin{array}{l}\frac{2\left(15\right)}{5}=\frac{1}{3}\left(2\left(15\right)-12\right)\\ 2\left(3\right)=\frac{1}{3}\left(30-12\right)\\ 6=\frac{1}{3}\left(18\right)\\ 6=6\end{array}$

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.