Chapter EP, Problem 1.4.19EP

To determine

To solve: The equation $7-\left|m-1\right|=3$ .

Answer to Problem 1.4.19EP

The solutions of the equation $7-\left|m-1\right|=3$ are $\left(5,-3\right)$ .

Explanation of Solution

Given:

The equation is $7-\left|m-1\right|=3$ .

Calculation:

Remove the mod from the equation.

  $\begin{array}{c}7-\left|m-1\right|=3\\ \left|m-1\right|=7-3\\ \left|m-1\right|=4\\ m-1=\pm 4\end{array}$

Simplify the equation $m-1=4$ .

  $\begin{array}{c}m-1+1=4+1\\ m=5\end{array}$

Simplify the equation $m-1=-4$ .

  $\begin{array}{c}m-1+1=-4+1\\ m=-3\end{array}$

Therefore, the solutions of the equation $7-\left|m-1\right|=3$ are $\left(5,-3\right)$ .

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

Substitute $m=5$ in the equation $7-\left|m-1\right|=3$ .

  $\begin{array}{c}7-\left|5-1\right|=3\\ 7-\left|4\right|=3\\ 3=3\\ \text{LHS}=\text{RHS}\end{array}$

Substitute $m=-3$ in the equation $7-\left|m-1\right|=3$ .

  $\begin{array}{c}7-\left|-3-1\right|=3\\ 7-\left|-4\right|=3\\ 3=3\\ \text{LHS}=\text{RHS}\end{array}$

So, the solutions $\left(5,-3\right)$ are correct.

Therefore, the solutions of the equation $7-\left|m-1\right|=3$ are $\left(5,-3\right)$ .