Q2B. - Algebra 1

Question

Solve the equation $\left|3n-4\right|=-1$. Also graph the solution set.

Step-by-Step Solution

Answer

On solving the equation $\left|3n-4\right|=-1$ the obtained solution set is an empty set, that is, $\varphi$. 

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 $\left|3n-4\right|=-1$, n is the variable which is the unknown quantity.

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 $\left|3n-4\right|=-1$.

The value of any absolute quantity should be positive but here, the value of $\left|3n-4\right|$ is $-1$. Also $\left|3n-4\right|=-1$ simply means that the distance between $3n$ and $1$ is $-1$, 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.