Chapter 8.2, Problem 46E

To determine

To solve:

The given equation. Check your solution.

Answer to Problem 46E

The solution of our given equation would be $n=42$ .

Explanation of Solution

Given:

An equation: $\frac{n}{6}+2=9$ .

Calculation:

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

  $\begin{array}{l}\frac{n}{6}+2=9\left(\text{Given equation}\right)\\ \frac{n}{6}+2-2=9-2\left(\text{Subtracting 2 from both sides}\right)\\ \frac{n}{6}=7\\ \frac{n}{6}\cdot 6=7\cdot 6\left(\text{Multiplying both sides by 6}\right)\\ n=42\end{array}$

Let us verify our answer by substituting $n=42$ in our original equation.

  $\begin{array}{l}\frac{n}{6}+2=9\\ \frac{42}{6}+2=9\\ 7+2=9\\ 9=9\end{array}$

Since both sides of equation are equal, therefore, $n=42$ is a solution of our given equation.