Chapter 6.3, Problem 64SR

To determine

To solve: the given equation and check the solution.

Answer to Problem 64SR

  $m=\frac{15}{10}$

Explanation of Solution

Given information:

Given solution

  $m-\frac{4}{5}=\frac{7}{10}$

Calculation:

If the same number is added to each side of an equation, the two sides remain equal.

  $\begin{array}{c}m-\frac{4}{5}=\frac{7}{10}\text{write}\text{the}\text{equation}\\ \underset{\_}{m-\frac{4}{5}+\frac{4}{5}=\frac{7}{10}+\frac{4}{5}}\text{Addition}\text{property}\text{of}\text{Equality}\\ \text{m+0=}\frac{7}{10}+\frac{4}{5}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{Additive}\text{inverse}\text{propeety;}-\frac{4}{5}+\frac{4}{5}\\ m=\frac{15}{10}\text{Additive}\text{inverse}\text{identity}\text{property};\end{array}$

Now, check as shown:

To check that $\frac{3}{2}$ is the solution, replace $m$ with $\frac{3}{2}$ in the original equation.

  $\begin{array}{l}m-\frac{4}{5}=\frac{7}{10}\\ \frac{15}{10}-\frac{4}{5}=\frac{7}{10}\text{Check}\text{to}\text{see}\text{whether}\text{this}\text{sentence}\text{is}\text{true}\text{.}\\ \frac{7}{10}=\frac{7}{10}\text{The}\text{sentence}\text{is}\text{true}\text{.}\end{array}$