Question

Solve each equation. Then graph the solution set.

$|p-4|=6$

Short answer

The solution set of the equation is$\{10,-2\}.$

The graph of the solution set is:

Step-by-step solution

Step 1. Given information.

We have an equation $|p-4|=6$.

To find the value of and plot the graph of solution.

Step 2. Apply concept.

We apply the concept of modulus function.

As$\left|x\right|=\left\{\begin{array}{c}xifx\le 0\\ -xifx>0\end{array}\right.$

Step 3. Calculation.

Here will exist two cases for the modulus function:

$\begin{array}{l}Case1:\\ p-4=6\\ p=6+4\\ p=10\\ Case2:\\ p-4=-6\\ p=-6+4\\ p=-2\end{array}$

Hence, the solution set of the given expression is $\{10,-2\}.$

The graph of the solution set: