# What is an Equation?

## Definition of equation

An equation is a statement that says that the value of two mathematical expressions is equal. In simple words, an equation says that two things are equal. It is denoted by the equal to sign ‘=’.

**Example of an Equation: **8+2= 12-2

The above equation says that the left side of the equation is equal to the right side. Thus an equation is a statement that states ‘this equals that’.

## Different types of equations in mathematics

Students may come across these different types of equations in Math, Algebra to be specific:

### 1. Linear equations

Linear means having one line. These are equations of the type Y= ax+b where ‘a’ and ‘b’ are numbers and ‘x’ cannot be zero. In these equations ‘x’ has no exponents. Y=4x+3 is a linear equation.

### 2. Quadratic equations

This is a second degree equation where one variable out of all contains the exponent of 2. ax2+bx+c= 0 is a quadratic equation where x is not equal to zero.

### 3. Radical equations

These are equations whose maximum exponent on the variable is ½ and have more than one term. Here the variable is lying inside a radical symbol usually in a square root. √x+10=26 is a radical equation.

### 4. Trigonometric equations

These are equations in which the variables are affected by trigonometric functions. Cos 2x= 1+Sin 4x is a trigonometric equation.

### 5. Polynomial equations

A polynomial equation is one which takes away the highest exponent limit. Here all the ‘x’s are numbers and the equation consists of several terms. (x7 + 2×4 – 5) * 3x=0

### 6. Exponential equations

These are equations that have variables in place of exponents. ab = 0 is an exponential equation.

## Solution of an equation

(x + 1)2 = x2 – 2

We need to first expand the variables on the left hand side of the equation with the formula of (a+b) 2= a2+ 2ab+ b2

X2+ 2x+ 1= x2-2

Now, x2 from both sides gets cancelled so we are left with

2x+1= -2

2x= -3

X= -3/2

X= -1.5

## Solve the following equations

1. 4+n= 6

a. 4 b. 2 c.10 d. 0

2. 4*7= v+9

a. 28 b. 9 c. 19 d. -19

3. m/10= 9*6

a. 5.4 b. 540 c.64 d. -5.4

4. 10*11= x-3

a. 110 b. -113 c. 113 d. 107

5. (-5-v)/3=1

a. -8 b. 8 c. 1.67 d. 15

6. 7= w-(-7)/5

a. 56 b. 5.6 c. 35 d. 3.5

7. 2p-6=8+5(p+9)

a. 19.6 b. -19.6 c. 59 d. -59

8. 8(x+4)-4= 4x-1

a. -7.25 b. 29 c. 7.25 d. 32

9. 8(t+5)+2= 4.8t+4

a. 1187 b.11.87 c. 11.78 d. -11.87

10. (3v/3) – 3v= -5

a. -2.5 b. 2.5 c. -6 c. 15