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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



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 < 3

Add the same number to both sides.

2 + 1 < 3 + 1

i.e. 3 < 4. It’s true.



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



Related Terms for Addition Property of Equality and Inequality





Equality

Inequality

Equation



Additional Links for Addition Property of Equality and Inequality



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