Chapter 6.3, Problem 67SR

To determine

To solve: the given equation and check the solution.

Answer to Problem 67SR

  $\frac{103}{14}=d$

Explanation of Solution

Given information:

Given solution

  $6\frac{4}{7}=d-\frac{11}{14}$

Calculation:

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

  $\begin{array}{c}6\frac{4}{7}=d-\frac{11}{14}\text{Write}\text{the}\text{equation}\\ \underset{\_}{6\frac{4}{7}+\frac{11}{14}=d-\frac{11}{14}+\frac{11}{14}}\text{Multiplication}\text{property}\text{of}\text{Equality}\\ 6\frac{4}{7}+\frac{11}{14}=d+0\text{Multiplication}\text{inverse}\text{property,-}\frac{11}{14}+\frac{11}{14}\\ \frac{46}{7}+\frac{11}{14}=d\text{Identity}\text{property }\\ \frac{103}{14}=d\end{array}$

Now, check as shown:

To check that $\frac{103}{14}$ is the solution, replace $d$ with $\frac{103}{14}$ in the original equation.

  $\begin{array}{c}6\frac{4}{7}=d-\frac{11}{14}\text{Write}\text{the}\text{equation}\\ 6\frac{4}{7}=\frac{103}{14}-\frac{11}{14}\\ 6\frac{4}{7}=\frac{103-11}{14}\\ 6\frac{4}{7}=6\frac{4}{7}\text{which is true}\end{array}$