Question

Solve each equation. (Lesson 2-5)

$\left|5p-8\right|=12$

Short answer

The solution set will be $c=-0.8\text{and}c=4$.

Step-by-step solution

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:$c=-0.8\text{and}c=4$

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

$\begin{array}{l}-(5c-8)=12\text{\hspace{0.33em}[Distribute]}\\ -5c+8=12\\ -5c+8-8=12-8\text{[Add-8tobothsides]}\\ -5c=4\\ -5c\times \left(-1\right)=4\times \left(-1\right)\text{[multiplyby-1bothsides]}\\ c=\frac{-4}{5}\\ c=-0.8\end{array}$

Step 3. Solve for a second possible solution.

We are given the expressions: $c=-0.8\text{and}c=4$

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

role="math" localid="1642665378941" $\begin{array}{l}5c-8=12\text{\hspace{0.33em}[Distribute]}\\ 5c-8+8=12+8\text{[Add-8tobothsides]}\\ 5c=20\\ c=\frac{20}{5}\\ c=4\end{array}$

Hence, the solution set will be $c=-0.8\text{and}c=4$.