ADDITION PROPERTY OF EQUALITY AND INEQUALITY

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 <>
Add the same number to both sides.
2 + 1 < 3="" +="" 1.="" it's="">

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

Quick Summary

Adding the same value to both sides of an equation maintains equality.
Adding the same value to both sides of an inequality maintains the inequality direction.

\[ Equality: If x = y, then x + z = y + z. Inequality: If x > y, then x + z > y + z and If x < y, then x + z < y + z. \]

🍎 Teacher Insights

Emphasize the concept of maintaining balance in equations and inequalities. Use real-world examples to illustrate the property. Provide plenty of practice problems.

🎓 Prerequisites

Basic arithmetic operations
Understanding of equations and inequalities
Concept of variables

Check Your Knowledge

Q1: Solve for x: x - 3 = 7

A. 4 B. 10 C. -4 D. -10

Q2: Solve for x: x - 2 < 5

A. x < 3 B. x > 3 C. x < 7 D. x > 7

Frequently Asked Questions

Q: Why does adding the same number to both sides maintain equality?
A: Because you're essentially performing the same operation on both sides, keeping the balance.

Q: Does the addition property work with negative numbers?
A: Yes, the addition property works for all real numbers, including negative numbers.