INEQUALITY

Inequality

Definition Of Inequality

An inequality is a mathematical sentence that uses symbols such as <, ≤,="">, or ≥ to compare two quantities.

Video Examples: How to Solve Inequalities

Example of Inequality

5 < d="">< 7,="" x="" ≥="" -="" 1,="">² ≤ b, - 12 > - 13 are few examples of inequalities

Solved Example on Inequality

Ques: Pick an appropriate graph for the inequality - 3 < x="" and="" x="">< 2="">

example of Inequality

Choices:

A. Figure 1
B. Figure 2
C. Figure 3
D. None of the above
Correct Answer: C

Solution:

Step 1: - 3 < x="">< 2="" [combine="" into="" one="">
Step 2: The compound inequality may be read as 'x is greater than - 3 and less than 2'.
Step 3: The graph of this compound inequality is
example of Inequality Step 4: So, Figure 3 represents the given inequality.

Quick Summary

Inequalities compare values.
They use specific symbols.
They can be graphed.

\[ a < b \]

⚠️ Common Mistakes

Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
Misinterpreting the symbols (e.g., confusing < with ≤).
Incorrectly graphing inequalities on a number line (open vs. closed circles).

📋 Standards Alignment

CCSS.MATH.CONTENT.6.EE.B.5
CCSS.MATH.CONTENT.7.EE.B.4

🍎 Teacher Insights

Use real-world examples to illustrate inequalities (e.g., speed limits, age restrictions). Emphasize the difference between open and closed circles on a number line when graphing.

🎓 Prerequisites

Number Sense
Basic Algebra
Graphing on a Number Line

Check Your Knowledge

Q1: Which symbol represents 'greater than or equal to'?

< > ≤ ≥

Q2: Solve for x: x + 3 < 7

x < 4 x > 4 x < 10 x > 10

Frequently Asked Questions

Q: What does the < symbol mean?
A: The < symbol means 'less than'.

Q: When do I flip the inequality sign?
A: You flip the inequality sign when you multiply or divide both sides by a negative number.