# Properties of Equality

The property that states that if you add the same number to both sides of an equation, the sides remain equal. Remember, whatever you do to one side you must do to the other. Let's look at this example: x - 12 = 2. Since 12 is a negative number in this equation add the +12 on both the sides. It will look like x - 12 + 12 = 2 + 12. So we are adding 12 to both sides. By looking at this expression we can say x = 14.

## Subtraction Property of Equality

States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal. Look at the example below. x + 100 = 200. Since 100 is a positive number in this equation, subtract 100 from 200 on both sides. This will look like x + 100 - 100 = 200 - 100. So we are subtracting 100 to both sides. By looking at this expression we can say x = 100.
Algebra 1 Substitution Method : Linear Algebra Education

## Multiplication Property of Equality

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal. The below example is 3x = 18.

How do you solve it? In this example you have to divide the same number both sides. See, in this example you will divide 3 by both sides which will look like 3x/3 =18/3. By looking at this expression we can say x = 6 .

## Division Property of Equality

Division Property of Equality states that dividing both sides of an equation by a non-zero number doesn't affect the equation.5p = 15
By dividing both sides of the equation by 5, we get p = 3.
Substituting p = 3 in the original equation will help us check the division property of equality.
5 x 3 = 15, it's true!