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.

Follow the below steps;**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.

Follow the below steps;**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.**