Chapter 2.1, Problem 23P

Solve each equation. Check your answer.

$-\frac{7}{8}=\frac{2}{3}+n$

To determine

To solve the equation:

  $\frac{-7}{8}=\frac{2}{3}+n$

And also check the solution.

Answer to Problem 23P

  $n=\frac{-37}{24}$

Explanation of Solution

Given:

  $\frac{-7}{8}=\frac{2}{3}+n$

Concept Used:

• Steps to solve a linear equation:
1. Use distributive property to remove any grouping symbol.
2. Simplify the expression in each side of the equation.
3. Collect the variable terms on one side of the equation and the constant on the other side.
4. Isolate the variable
• To check the solution of a equation substitute the solution in the equation and check whether it satisfies.

Calculation:

In order to solve the equation:

  $\frac{-7}{8}=\frac{2}{3}+n$

First, simplify each side of the equation by isolating the variable which is done by subtracting $\frac{2}{3}$ on both sides as,

  $\begin{array}{l}\frac{-7}{8}-\frac{2}{3}=\frac{2}{3}-\frac{2}{3}+n\\ \Rightarrow \frac{-21-16}{24}=n\\ \Rightarrow n=\frac{-37}{24}\end{array}$

Thus, solution of given equation is $n=\frac{-37}{24}$ .

Now, to check this solution put $n=\frac{-37}{24}$ in right hand side of the given equation, and check whether both sides are equal. As,

  $\begin{array}{c}\frac{2}{3}+\left(\frac{-37}{24}\right)=\frac{2}{3}-\frac{37}{24}\\ =\frac{48-111}{72}\\ =\frac{-63}{72}\\ =\frac{-7}{8}\\ =\text{Left hand}\end{array}$

Thus, $n=\frac{-37}{24}$ is correct solution for given equation.