# Equation in Math

In this chapter we will learn the concept of equation, its definition and some solved problems.

## What is Equation in Math?

When a math expression contains equal to sign ” = ” , it is termed as an equation.

In equation, the expression present in left side of “=” symbol is equal to the right side.

Examples of equation;

(i) 4x + y = 6

The above expression contains ” = ” sign, hence its an example of equation.

Left side of equation is 4x + y

Right side of equation is 6.

The equation tells us that value of 4x + y is equal to 6.

(ii) 10x + 3y + x + 4 = 11

Since the expression contains ” = ” symbol, it is an example of equation.

Left side of equation is 10x + 3y + x + 4

Right side of equation is 11

The equation tells that value of 10x + 3y + x + 4 is equal to 11.

(iii) 6x + 2y + 3 = 11x + 1

The expression contains ” = ” sign, hence it is a math equation.

Left side of equation is 6x + 2y + 3

Right side of equation is 11x + 1

The equation tells that value of left side ( 6x + 2y + 3 ) is equal to the value of right side (11x+ 1)

(iv) 6x -7 + 4y

This expression is not an equation since it do not contain ” = ” sign.

### Solving the equation

Solving the equation basically involves finding the values of variable to satisfy the given equation.

For Example
Consider the equation 2x + 3 = 9

To solve the equation you have to find the value of variable x so that left side becomes equal to right side.

Given below are steps to find x value.

Step 01
Take number 3 to right side. While taking number 3 to the right, the addition becomes subtraction.

2x + 3 = 9

2x = 9 – 3

2x = 6

Step 02
Take number 2 on right side. While taking number 2 on right, multiplication becomes division.

2x = 6

x = 6 / 2

x = 3

Hence for given equation, the value of x is 3.

Validation
Put x = 3 in the equation 2x + 3 = 9

2 (3) + 3 = 9

6 + 3 = 9

9 = 9

Hence both side equals 9. This means that for x = 3, the equation gets satisfied.

## Equations – Solved Problems

(01) Solve the given equations

(i) y + 10 = 15
(ii) 9x + 4 = 31
(iii) z – 13 = 50
(iv) 4y – 7 = 13
(v) 3y -16 = 2

Solution

(i) y + 10 = 15

To solve the equation, we have to find the value of variable y.

Step 01
Move number 10 to right side. On moving the number to other side, the addition becomes subtraction.

y + 10 = 15

y = 15 – 10

y = 5

Hence, the value of variable y is 5.
It means that when we put number y = 5, the equation will be satisfied.

(ii) 9x + 4 = 31

To find the value of x, follow the below steps;

Step 01
Move number 4 to right. While moving number to other side, the addition becomes subtraction.

9x + 4 = 31

9x = 31 – 4

9x = 27

Step 02
Move number 9 to right. Here the multiplication becomes division.

9x = 27

x = 27 / 9

x = 3

Hence, the value of x is 3.

(iii) z – 13 = 50

Here we have to find the value of variable z.

Move number 13 to right.
While moving other side, the subtraction becomes addition.

z – 13 = 50

z = 50 + 13

z = 63

Hence, the value of variable z is 63.

(iv) 4y – 7 = 13

Here we have to find the value of variable y.

Step 01
Move number 7 to right.
While moving, the subtraction becomes addition.

4y = 13 + 7

4y = 20

Step 02
Move number 4 to right.
Here the multiplication becomes division.

4y = 20

y = 20/4

y = 5

Hence in given equation, the value of variable y is 5.

(v) 3y -16 = 2

To find value of y, follow the below steps.

Step 01
Move number 16 to right.
While moving the subtraction becomes addition.

3y – 16 = 2

3y = 2 + 16

3y = 18

Step 02
Now move number 3 to right.
Here the multiplication becomes division.

3y = 18

y = 18 / 3

y = 6

For given equation, the value of y is 6.