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.="">
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