# Linear Equation in One Variable Class 8

An equation is defined as a mathematical statement. An equation has two expressions, each expression is separated by an equal sign (=).  Linear equations play a very important role in middle-level and higher-level mathematics. Linear equations in one variables are quite commonly used and easy to deal with. A lot can be said about linear equations. Linear equation in one variable topic is introduced to Class 8 students. We have designed some of the questions with the help of subject experts to clear Class 8 student's concepts on the topic. As we know, not only practice significantly increase your speed of solving problems but one must have good knowledge of concepts.  This section aims to provide an overview of key aspects of linear equations in one variable to help with your efforts.

## Steps to Solve

Solving an equation means to evaluate the value of the variable. In order to solve linear equations in one variable, one needs to keep few points in mind:
1. Follow BODMAS rule, where B stands for brackets, D for division, M for multiplication, A for addition and S for subtraction.
2. Keep the variable on left hand side and all constants on right hand side.
3. Always look at the sign before a variable or constant and then follow the above rules.

## Solving Linear Equations Two Step

Two Step Equations are defined as solving an equation applying two rules. This is called so because, there are only two operations needed to solve the equation.

Facts to remember
1. Opposite of addition operation is subtraction and vice versa.
2. Opposite of multiplication operation is division and vice versa.

Two types of such equations can be defined
2-Step Multiplication Equations
2-Step Division Equations
2-Step Multiplication Equations

The process for solving 2 step multiplication equations is as follows:
1. Add or subtract terms from both sides, so that, the Coefficient and Variables are on either side of the equal sign.
2. Divide both sides by the coefficient of the variable.
3. Solve the equation.

Examples on 2-Step Multiplication Equations

For Example, 8x + 5 = 21

Solution: To solve, the variable must be on one side and all the other numbers must be on the other side:
8x + 5 = 21
Subtract 5 from both the sides
8x + 5 - 5 = 21 - 5
8x + 0 = 16
8x = 16
Divide both the sides by 8

$\frac{8x}{8}$ = $\frac{16}{8}$

x = 2

2-Step Division Equations

The process for solving a 2 step division equation is as follows:
Add or subtract terms from both sides, so that, the Coefficient and Variables are on either side of the equal sign.
Multiply both the sides by the coefficient of the variable.
Solve the equation.

Examples on 2-Step Division Equations

For Example, $\frac{x}{3}$ - 5 = 22

Solution: To solve, the variable must be on one side and all the other numbers on the other side.
$\frac{x}{3}$ - 5 = 22

Add 5 on both the sides
$\frac{x}{3}$ - 5 + 5 = 22 + 5

$\frac{x}{3}$ = 27

Multiply both the sides by 3
$\frac{3x}{3}$ = 3 × 27

x = 81

## Examples on Solving Equations

Given below are some examples that explain how to solve equations.

Example 1: Solve 7x = 6x +1

Solution: Given equation 7x = 6x +1

7x - 6x = 6x - 6x + 1 (Subtract 6x from both the sides of the equation.)

x = 1

Example 2: Solve 12x - 6 = 6x + 12

Solution:

12x - 6 = 6x + 12

12x - 6x - 6 = 6x - 6x + 12 (Subtract 6x from both the sides of the equation.)

6x - 6 = 12

6x - 6 + 6 = 12 + 6 (Add 6 to both sides)

6x = 18

$\frac{6x}{6}$ = $\frac{18}{6}$  (Divide by 6 on both sides)

x = 3

Example 3: Find the value of x.
3x + 5x = 4

Solution: 3x + 5x = 4

8x = 4

x = $\frac{1}{2}$

## Applications of Linear Equations in One Variable

Linear equations in one variable are widely applicable in middle and higher level mathematics. There is a vast variety of word problems based on linear equations in one variable that are used in algebra, arithmetic, geometry, calculus, coordinate geometry etc.

Not only in mathematics, these equations are to be seen quite often in different other branches, like - physics, chemistry, economics, commerce, engineering etc. Many computer programs are also based upon linear equations in one variables.

Basically, these equations are one of the most essential part of pure and applied mathematics. Also, linear equations with one variables are quite useful in real life situations.

## Word Problem for Class 8

Example: If the ratio of two numbers be 2 : 5 and their difference is 18. Calculate both the numbers.
Solution: Let us suppose that the numbers are 2x and 5x.
According to the given condition:
Difference = 18
5x - 2x = 18
3x = 18
x = $\frac{18}{3}$
x = 6
Therefore the number will be
2x = 12
and
5x = 30.

Cross check
Ratio = $\frac{12}{30}$
= 2 : 5
Difference = 30 - 12 = 18

## Practice Problems

Question 1: Solve 3x - 18 = 15x + 10
Question 2: Find the value of m. m - 1/3 = 12m + 10
Question 3: Solve for x. 13x - 5 + x  = -11 + x