Question

Solve each equation. Then graph the solution set.

$\frac{4}{\left|p\right|}+12=14$

Short answer

The equation $\frac{4}{\left|p\right|}+12=14$has solution set as $p=2,-2$and the graph of the solution set is:

Step-by-step solution

Step-1. Define absolute value equation.

For any real numbers a and b, if$\left|a\right|=b$ and $b\ge 0$, then$a=b$ or $a=-b$.

Step-2. Formulate case 1 when p=p.

Simplify the expression for p.

$\begin{array}{c}\frac{4}{p}+12-12=14-12\\ \frac{4}{p}\times p=2\times p\\ 4=2p\\ \frac{4}{2}=\frac{2p}{2}\\ p=2\end{array}$

Step-3. Formulate case 2 when p=−p.

Simplify the expression for p.

$\begin{array}{c}\frac{4}{\left(-p\right)}+12-12=14-12\\ \frac{4}{\left(-p\right)}\times \left(p\right)=2\times p\\ -4=2p\\ \frac{-4}{2}=\frac{2p}{2}\\ p=-2\end{array}$

Step-4. Plot the graph of the solution set.

From case 1 and case 2, $p=2,-2$. Plot these values on the number line.