# Equation

A statement that asserts the equality of two mathematical expressions.

## Introduction

In mathematics, a changeable quantity is written as a mathematical expression. If two mathematical expressions represent same quantity, then they are equal mathematically. The equality of them is symbolically denoted by displaying an equal symbol ($=$) between both mathematical expressions. The equality of both mathematical expressions is called an equation.

### Example Let’s consider a boy and his little sister. The heights, weights and genders of them are different and they cannot be expressed in mathematical form because they will be changed every time and they don’t have proper relation. However, the age difference between them is always constant. So, it can be expressed in mathematical form.

The ages of boy and his sister are unknown but the boy is $3$ years older than his sister. So, take

1. The age of boy is $x$ years.
2. The age of his sister is $y$ years.

If the number $3$ is added to age of the girl, then it is equal to the age of the boy. Mathematically, the equality between them is symbolically represented by an equal symbol.

$x = y+3$

This mathematical statement expresses the equality of two mathematical expressions. Hence, it is called an equation.

#### Examples

Here is some of the example equations in mathematical form for your knowledge.

$(1) \,\,\,\,\,\,$ $3x^2-2x+8 = 0$

$(2) \,\,\,\,\,\,$ $7\log_{5}{x}+4 = 5\log_{5}{x}$

$(3) \,\,\,\,\,\,$ $4\sin{x}\tan{x}+3\cos{x} = 9\tan{x}$

$(4) \,\,\,\,\,\,$ $-e^{5y}+e^{2y}-6 = 4e^y$

$(5) \,\,\,\,\,\,$ $4\dfrac{d^3y}{dx^3}-3\dfrac{dy}{dx}-8 = 0$

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