Linear Equations in One Variable: Definition and Formula

Linear Equations in One Variable: In Mathematics, equations having one degree are known as linear equations in one variable. The equation has an equality sign where the expression on the left is called left hand side and the expression on the right is called right hand side. For example, 2x + 3= 6 where x is the one variable and 2 & 3 are the real numbers.

This is a very important concept in algebra where students learn to solve mathematical equations easily. You can check NCERT Solutions for Class 8 Maths for a better understanding of the concept. We have provided detailed information on linear equations in one variable in this article. Read on to find out about its definition, formula and examples.

Linear Equation in One Variable: Definition

An equation that has only one degree, i.e., the highest power of the variable in the equation is one is called a linear equation in one variable. Solving linear equations is based on having rational as its solution and variable on both sides. You can calculate problems related to age, perimeter, combination of currency notes etc. We can say that values of expression on right hand side and left hand side are equal. Therefore, these values are called solutions.

Solving Linear Equations In One Variable: Formula

The formula used to calculate linear equation in one variable is mentioned below:

ax + b = 0

Where x is a variable and a & b are the real numbers

Download NCERT Solutions for Class 8 Maths Chapter 2 PDF

Linear Equation In One Variable: Examples

Some of the examples of linear equation in one variable from the NCERT Textbook are given below:

Example 1: Arjun is twice as old as Shriya. Five years ago his age was three times Shriya’s age. Find their present ages.

Solution: Let us take Shriya’s present age to be x years.

Then Arjun’s present age would be 2x years.

Shriya’s age five years ago was (x – 5) years.

Arjun’s age five years ago was (2x – 5) years.

It is given that Arjun’s age five years ago was three times Shriya’s age.

Thus, 2x – 5 = 3(x – 5) or 2x – 5 = 3x – 15 or 15 – 5 = 3x – 2x or 10 = x

So, Shriya’s present age = x = 10 years.

Therefore, Arjun’s present age = 2x = 2 × 10 = 20 years.

Example 2: Find the solution of 2x – 3 = 7

Solution: Add 3 to both sides.

2x – 3 + 3 = 7 + 3

or 2x = 10

FAQs On Linear Equation In One Variable

The frequently asked questions on linear equation in one variable are given below:

Q. What is linear equation in one variable?
A. An equation that has only one degree, i.e., the highest power of the variable in the equation is one is called a linear equation in one variable.

Q. What is the formula of linear equation in one variable?
A. The formula used for calculating the equation is ax + b = 0 Where x is variable and a & b are the real numbers.

Q. What are solutions in an equation?
A. The values of expression on right hand side and left hand side are equal. Therefore, these values are called solutions.

Now we have provided detailed information in this article. You can solve the CBSE Class 8 practice questions on Embibe for Mathematics and Science. You can also take CBSE Class 8 Mock Tests for these subjects. These will be of great help to you. You should also download NCERT Class 8 Maths Chapter 2 PDF available on this page.

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