Chapter 8.6, Problem 37E

To determine

To solve:

The given equation. Check your solution.

Answer to Problem 37E

The solution of our given equation would be $m=8$ .

Explanation of Solution

Given:

An equation: $4(m-4)=2m$ .

Calculation:

To solve our given equation, we use opposite operations as shown below:

  $\begin{array}{l}4(m-4)=2m\left(\text{Given equation}\right)\\ 4m-16=2m\left(\text{Using distributive property}\right)\\ 4m-16+16=2m+16\left(\text{Adding 16 on both sides}\right)\\ 4m=2m+16\\ 4m-2m=2m-2m+16\left(\text{Subtracting }2m\text{ on both sides}\right)\\ 2m=16\\ \frac{2m}{2}=\frac{16}{2}\left(\text{Dividing both sides by }2\right)\\ m=8\end{array}$

Let us verify our answer by substituting $m=8$ in our original equation.

  $\begin{array}{l}4(m-4)=2m\left(\text{Given equation}\right)\\ 4(8-4)=2(8)\left(\text{Substituting }m=8\right)\\ 4(4)=16\\ 16=16\end{array}$

Since both sides of equation are equal, therefore, $m=8$ is a solution of our given equation.