Question

Solve equation $\left|5h+2\right|=-8$and then graph the solution set.

Short answer

On solving $\left|5h+2\right|=-8$the obtained solution set is an empty set, that is,$\varphi$.

Step-by-step solution

Step-1. Apply the concept of Variables and constant.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

In $\left|5h+2\right|=-8$, h is a variable.

Constants: - In any expression or equation constant are the values which is fixed.

While performing addition in an equation, same kind of elements or like terms are added together.

Step-2. Concept of absolute value.

Absolute value: - Absolute value of any quantity simply means positive value of that quantity.

Example: -

Consider a variable x. Here x can be both positive or negative but $\left|x\right|$will always be positive and hence the absolute value.

Step-3. Solution of the given equation.

Given $\left|5h+2\right|=-8$.

The value of any absolute quantity should be positive but here, the value of $\left|5h+2\right|$is $-8$. Also $\left|5h+2\right|=-8$simply means that the distance between $5h$and 2 is $-8$, which is not possible at all as distance can’t be negative.

Hence the solution set is empty, which is represented as .

Step-4. Graph of the solution set.

Consider a number line as h.