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, its true

  • Addition Property of Inequality

a) 2 < 3

Add the same number to both sides,

2 + 1 < 3 + 1

3 < 4, its 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