Solve each equation. (Lesson 2-5)

$\left|2p-3\right|=17$

The absolute value or modulus of a real number x denoted |x| is the non-negative value of x without regard to its sign.

Absolute value refers to a point's distance from zero or origin on the number line, regardless of the direction.

We are given the expressions:$|2p-3|=17$

Since an absolute function value can never be negative we have two scenarios that are possible.

Case: 1 when expression inside the modulus sign is negative, that is

role="math" localid="1642664720960" $\begin{array}{l}-(2p-3)=17\text{\hspace{0.33em}[Distribute]}\\ -2p+3=17\\ -2p+3-3=17-3\text{[Add-3tobothsides]}\\ -2p=14\\ -2p\times \left(-1\right)=14\times \left(-1\right)\text{[multiplyby-1bothsides]}\end{array}$

$\begin{array}{l}2p=-14\\ p=\frac{-14}{2}\\ p=-7\end{array}$

We are given the expressions: $|2p-3|=17$

Case: 2 when expression inside the modulus sign is positive, that is

role="math" localid="1642664857683" $\begin{array}{l}2p-3=17\\ 2p-3+3=17+3\text{[Add3tobothsides]}\\ 2p=20\\ p=\frac{20}{2}\\ p=10\end{array}$

Hence, the solution set will be $p=-7\text{and}p=10$.