## Related Words

# Addition Property of Equality and Inequality

## 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 < y, then x + z < y + z.

### Examples of Addition Property of Equality and Inequality

- a) 3 = 3
- Add the same number to both sides.
- 3 + 2 = 3 + 2. It's true.

**Addition Property of Equality:**

- a) 2 < 3
- Add the same number to both sides.
- 2 + 1 < 3 + 1. It's true.

**Addition Property of Inequality:**

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

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

#### 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

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