Chapter 5.5, Problem 41E

To determine

To solve:the equation $1=2+\frac{n}{-7}$ and check the solution.

Answer to Problem 41E

The solution of the equation $1=2+\frac{n}{-7}$ is $7=n$

Explanation of Solution

Given information:

The provided equation is $1=2+\frac{n}{-7}$ .

Calculation:

To solve the given equation, follow the steps given:

  $\begin{array}{l}1=2+\frac{n}{-7}\text{ [Write the original equation]}\\ 1-2=2+\frac{n}{-7}-2\left[\text{Subtract both side by 2}\right]\\ -1=\frac{n}{-7}\left[\text{Simplify}\right]\\ \left(-7\right)\cdot -1=\left(-7\right)\cdot \frac{n}{-7}\text{ [Multiply both side by }\left(-7\right)\text{] }\\ 7=n\left[\text{Simplify}\right]\end{array}$

To check the solution substitute the value $7=n$ in the expression $2+\frac{n}{-7}$ and is the results is equals to 1, that is, if left-hand side is equals to right-hand side then the solution is correct.

  $\begin{array}{l}2+\frac{n}{-7}\left[\text{Write the original expression}\right]\\ =2+\frac{7}{-7}\left[\text{Substitute the value of }n\right]\\ =\frac{2\cdot \left(-7\right)}{-7}\text{+}\frac{7}{-7}\left[\text{Write the fraction using LCD}\right]\\ \text{=}\frac{-14+7}{-7}\left[\text{Write numerator over denominator}\right]\\ =\frac{-7}{-7}\left[\text{Add}\right]\\ =1\left[\text{Simplify}\right]\end{array}$

Hence, the solution of the given equation is $7=n$ and correct.