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Inequalities

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Inequalities

Study Guide

Key Definition

Inequalities compare two quantities using ordering symbols like $<$, $>$, $\leq$, and $\geq$. The symbol $\neq$ means not equal but does not indicate an order.

Important Notes

Inequalities show relationships where quantities are not equal.
Use an open dot for $<$ and $>$ on number lines.
Use a closed dot for $\leq$ and $\geq$ on number lines.
Compound inequalities combine two inequalities.
Graphing solutions helps visualize inequalities.
When multiplying or dividing both sides by a negative number, reverse the inequality symbol.

Mathematical Notation

$\neq$ means not equal to

$<$ means less than

$>$ means greater than

$\leq$ means less than or equal to

$\geq$ means greater than or equal to

Remember to use proper notation when solving problems

Why It Works

Inequalities allow us to describe ranges of values and relationships, which is crucial in problem-solving and real-world applications.

Remember

Inequalities help us understand how quantities relate to each other with $inequality symbols$.

Quick Reference

Strict Inequality:$<$ or $>$

Non-strict Inequality:$\leq$ or $\geq$

Understanding Inequalities

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

An inequality shows that one quantity is less than or greater than another. For example, $x < 3$ means x can be any number smaller than 3, and $x > 3$ means x is any number greater than 3.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which inequality represents x less than 5?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A store offers a discount for purchases over $20. Write an inequality to represent this situation.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Solve the inequality $2x + 3 < 7$.

Challenge Quiz

Single Choice Quiz

Advanced

Which inequality represents the solution to $3(x - 2) \geq 9$?

Recap

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Review key concepts and takeaways