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

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.

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.

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 $\varphi$.

Consider a number line as n.