SUBTRACTIVE PROPERTY OF EQUATIONS AND INEQUALITIES

Subtractive Property Of Equations And Inequalities

Definition Of Subtractive Property Of Equations And Inequalities

Subtractive Property of Equations: If the same number is subtracted from both sides of an equation, then the two sides remain equal. That is, if x = y, then x - z = y - z.

Subtractive Property of Inequalities: Subtracting the same number from 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.

Video Examples: Solving Inequalities with Addition and Subtraction | Algebra 1 How to Help

Example of Subtractive Property of Equations and Inequalities

Addition Property of Equality:
a) 3 = 3
Subtract the same number from both sides,
3 - 2 = 3 - 2, its true
Addition Property of Inequality:
a) 2 <>
Subtract the same number from both sides,
2 - 1 < 3="" -="">
< 2,="" its="">

Solved Example on Subtractive Property of Equations and Inequalities

Ques: If a + 15 = 10, then what is the value of a?

Choices:

A. - 5
B. - 15
C. 5
D. 15
Correct Answer: A

Solution:

Step 1: a + 15 = 10 [Given.]
Step 2: a + 15 - 15 = 10 - 15 [Subtract - 15 from both the sides.]
Step 3: a = - 5

Quick Summary

Subtracting the same value from both sides maintains equality in equations.
Subtracting the same value from both sides preserves the inequality's direction.

\[ If x = y, then x - z = y - z. If x < y, then x - z < y - z. If x > y, then x - z > y - z. \]

🍎 Teacher Insights

Use visual aids like balances to demonstrate the concept of equality. Emphasize the 'do the same to both sides' rule. Provide ample practice problems.

🎓 Prerequisites

Basic Algebra
Understanding of Equality and Inequality

Check Your Knowledge

Q1: If x + 5 = 12, what is the value of x?

A. 7 B. 17 C. 60 D. -7

Q2: If y - 3 > 8, what is a possible value for y?

A. 5 B. 11 C. 2 D. -11

Frequently Asked Questions

Q: Why does the Subtractive Property work?
A: It maintains the balance in an equation or the relationship in an inequality. If you change one side, you must change the other identically to keep the statement true.

Q: Can I subtract variables from both sides?
A: Yes, as long as you subtract the same variable expression from both sides.