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:$c=−0.8\text{and}c=4$

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

$\begin{array}{l}−(5c−8)=12\text{ [¶Ù¾±²õ³Ù°ù¾±²ú³Ü³Ù±ð±Õ}\\ −5c+8=12\\ −5c+8−8=12−8\text{[Add-8tobothsides]}\\ −5c=4\\ −5c×\left(−1\right)=4×\left(−1\right)\text{[multiplyby-1bothsides]}\\ c=\frac{−4}{5}\\ c=−0.8\end{array}$

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" $\begin{array}{l}5c−8=12\text{ [¶Ù¾±²õ³Ù°ù¾±²ú³Ü³Ù±ð±Õ}\\ 5c−8+8=12+8\text{[Add-8tobothsides]}\\ 5c=20\\ c=\frac{20}{5}\\ c=4\end{array}$

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