Chapter EP, Problem 1.4.9EP

To determine

To solve: The equation $\left|d+1\right|=7$ .

Answer to Problem 1.4.9EP

The solutions of the equation $\left|d+1\right|=7$ are $\left(6,-8\right)$ .

Explanation of Solution

Given:

The equation is $\left|d+1\right|=7$ .

Calculation:

Remove the mod from the equation.

  $d+1=\pm 7$

Simplify the equation $d+1=7$ .

Subtract 1 from both sides of the equation $d+1=7$ .

  $\begin{array}{c}d+1-1=7-1\\ d=6\end{array}$

Simplify the equation $d+1=-7$ .

Subtract 1 from both sides of the equation $d+1=-7$ .

  $\begin{array}{c}d+1-1=-7-1\\ d=-8\end{array}$

Therefore, the values of the equation $\left|d+1\right|=7$ are $\left(6,-8\right)$ .

To check the solution, substitute these values in the original equation.

Substitute $d=6$ in the equation $\left|d+1\right|=7$ .

  $\begin{array}{c}\left|6+1\right|=7\\ \left|7\right|=7\\ 7=7\\ \text{LHS}=\text{RHS}\end{array}$

Substitute $d=-8$ in the equation $\left|d+1\right|=7$ .

  $\begin{array}{c}\left|-8+1\right|=7\\ \left|-7\right|=7\\ 7=7\\ \text{LHS}=\text{RHS}\end{array}$

So, the solutions $\left(6,-8\right)$ are correct.

Therefore, the solutions of the equation $\left|d+1\right|=7$ are $\left(6,-8\right)$ .