Question

Solve equation $\left|4n-1\right|=-6$and then graph the solution set.

Short answer

On solving $\left|4n-1\right|=-6$the obtained solution set is an empty set, that is, $\varphi$and the respective graph will be: -

The graph of the solution is: -

Step-by-step solution

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

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

In $\left|4n-1\right|=-6$, n is a variable.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the 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 a 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 $\left|4n-1\right|=-6$.

The value of any absolute quantity should be positive but here, the value of $\left|4n-1\right|$is $-6$. Also, $\left|4n-1\right|=-6$simply means that the distance between $4n$and 1 is $-6$, which is not possible at all as distance can’t be negative.

Hence, the solution set is empty, which is represented as $\varphi$.

Step-4. Graph of the solution set.

Consider a number line as n.