Q20. - Algebra 1

Question

Solve each equation. Check your solution.

$3\left(3m-2\right)=2\left(3m+3\right)$

Step-by-Step Solution

Answer

The solution of the given equation is $m=4$.

Step 1. Write the given equation.

The given equation is “$3\left(3m-2\right)=2\left(3m+3\right)$”.

Step 2. Solve the given equation.

Solving,

$3\left(3m-2\right)=2\left(3m+3\right)$  (Given equation)

$9m-6=6m+6$  (Distributive property)

$9m-6-6m=6m+6-6m$  (Subtract $6m$ from both sides)

$3m-6=6$  (Simplify)

$3m-6+6=6+6$  (Add 6 to both sides)

$3m=12$  (Simplify)

$\frac{3m}{3}=\frac{12}{3}$  (Divide both sides by 3)

$m=4$  (Simplify)

So, $m=4$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $m=4$ in the given equation $3\left(3m-2\right)=2\left(3m+3\right)$ to get,

$\begin{array}{l}3\left(3\left(4\right)-2\right)=2\left(3\left(4\right)+3\right)\\ 3\left(12-2\right)=2\left(12+3\right)\\ 3\left(10\right)=2\left(15\right)\\ 30=30\end{array}$

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.