## What is an Equation?

An equation is a mathematical statement stating the equality of two mathematical expressions. An equation is usually written as a **meaningful linear array of mathematical symbols** that has left and right sides and is connected by an equal sign.

** **

**(x – 3)/2=7** is an equation but **) x (3-/2=7** is not because in the second example, the mathematical symbols do not form a meaningful linear array.

## What is a Linear Equation?

A linear equation is an equation in which the highest exponent of the variable / variables is **1. **For example **(x-3)/2=7** is a linear equation but **(x2 -3)/2=7** is not because the power of **x **is **2**. It is called “linear” because the graph between any of the two variables will be a straight line. In the second example, because negative numbers squared are the same as the positive counterpart squared, make two *x*-coordinate values for each *y*.

When teaching linear equations, remind students that for a linear equation to be true, the left side must be equal to the right side.

## Fundamentals for Solving and Teaching Linear Equations

**The Equality Property for Addition and Subtraction:**If two expressions are equal then adding or subtracting equal numbers to both sides does not change that equality.

For exampl**e, **If ** m = n** then,

**and**

*m+c = n+c*

*m-d = n-d***The Equality Property for Multiplication and Division:**If two expressions are equal then multiplying or dividing by any equal number except zero on both sides does not change that equality.

For example, if ** m=n** then,

**and**

*m/c = n/c***where**

*m x d = n x d***is not equal to**

*c***.**

*zero***The Rule of Inverse: Addition**and**subtraction**are inverse to each other, which means if some number is added to one side of a linear equation and you want to take it to the other side then you have to subtract the number from both sides.

For example, in the equation ** x – 3 = 7 **if you want to take

**3**to the right side then you have to

**add**both the side with

**3**and the linear equation will become

**x = 10.**

Similarly, **multiplication** and **division** are inverse to each other.

For example, **(x – 3)/2 = 7** here we can take** 2** on the right hand side by multiplying both sides by **2**.

## Solving a Linear Equation with One Variable

**Simplify:**1.

2. Use the distributive property to remove parenthesis.

**Use equality properties:**Use equality properties for addition/subtraction and multiplication/division to move numbers (constants) to one side.

**Example:**

**(x – 3)/2 = 7 **

**or, x/2 – 3/2 = 7 (using distributive property for removing parenthesis)**

**or, x – 3 = 14 (using equality property for multiplication/division and multiplying by 2 on both the sides)**

**or, x = 17 (using equality property for addition/subtraction and adding 3 on both the sides)**