Q57. - Algebra 1

Question

Solve each equation. (Lesson 2-5)

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

Step-by-Step Solution

Answer

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

Step 1. Use the definition of the absolute value function.

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. 

Step 2. Solve for the first possible solution.

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

$\begin{array}{l} -(2p-3)=17\text{\hspace{0.33em} [Distribute]}\\ -2p+3=17\\ -2p+3-3=17-3\text{ [Add -3 to both sides]}\\ -2p=14\\ -2p\times \left(-1\right)=14\times \left(-1\right)\text{ [multiply by -1 both sides]}\end{array}$

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

Step 3. Solve for a second possible solution.

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

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

  $\begin{array}{l} 2p-3=17\\ 2p-3+3=17+3\text{ [Add 3 to both sides]}\\ 2p=20\\ p=\frac{20}{2}\\ p=10\end{array}$

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