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 <>, 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. Itís true.

    Addition Property of Inequality
    a) 2 <>
    Add the same number to both sides.
    2 + 1 < 3="" +="">
    i.e. 3 < 4.="" itís="" 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