91Ó°ÊÓ

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" $\begin{array}{l}−(2p−3)=17\text{ [¶Ù¾±²õ³Ù°ù¾±²ú³Ü³Ù±ð±Õ}\\ −2p+3=17\\ −2p+3−3=17−3\text{[Add-3tobothsides]}\\ −2p=14\\ −2p×\left(−1\right)=14×\left(−1\right)\text{[multiplyby-1bothsides]}\end{array}$

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

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 $p=−7\text{and}p=10$.