### Simple Equations

Equations involving only a linear polynomial are called simple equations.

e.g. 4x + 5 = 65, 10y – 20 = 50

In an equation, there is always an equality sign.

A Simple Equation remains the same when the expression in the left and right are interchanged.

The value of a variable, which makes the equation a true statement is called the solution of a linear equation.

e.g. 5x – 12 = -2 is a equation

L.H.S = 5x – 12 = 5 × 2 – 12 = 10 – 12 = -2

L.H.S = R.H.S

#### Variables and Expressions

**Variable **is a quantity that can take any value, its value is** not fixed**. It is a symbol for a number whose value is unknown yet.

**Expressions** are formed by performing operations like **addition, subtraction, multiplication** and **division** on the variables.

Example: 6x – 3 is an expression in variable x.

### Algebraic Equation

An **equation** is a **condition on a variable** such that two expressions in the variable should have **equal value**.

Example: 8x−8=16 is an equation.

The **value** of the **variable** in an equation for which the** equation is satisfied** is called the **solution of the equation**.

Example: The solution for the equation 2x−3=5 is x=4.

### Mathematical Operations on Expressions

- Addition of variables: (3x+4z)+(5y+6)
- Subtraction of variables: (4x−7y)−(6y+5)
- Multiplication of variables: (5xy+6)×7x
- Division of variables: (8xz+5z)/(5x-6y)