# Addition Property of Equality and Inequality

## Related Words

## Definition of Addition Property of Equality and Inequality

**Addition Property of Equality:**

If the same number is added to both sides of an equation, the two sides remain equal.

That is, if x = y, then x + z = y + z.

**Addition Property of Inequality:**

Adding the same number to both sides of an inequality does not affect the inequality.

That is,
if x > y, then x + z > y + z, and
if x <>, then x + z < y="" +="">.

### Examples of Addition Property of Equality and Inequality

Addition Property of Equality

a) 3 = 3

Add the same number to both sides.

3 + 2 = 3 + 2. It’s true.

Addition Property of Inequality

a) 2 <>

Add the same number to both sides.

2 + 1 < 3="" +="">

i.e. 3 < 4.="" it’s="" true.="">

### Video Examples: Addition property of equality and inequality

### Solved Example on Addition Property of Equality and Inequality

**Ques: **

Solve for x:

x - 5 = 12

##### Choices:

A. 7

B. 17

C. - 7

D. 2.4

Correct Answer: B

#### Solution:

Step 1: x - 5 = 12

Step 2: x - 5 + 5 = 12 + 5

Step 3: x = 17