Introduction to Inequalities

Learn the basics of inequalities and how to compare values using inequality symbols.

Intermediate20 minLesson

Definition

An inequality is a mathematical statement that compares two values that are not necessarily equal.

We use these symbols to show relationships:

Symbol	Meaning	Example
	Less than	(3 is less than 5)
	Greater than	(7 is greater than 2)
	Less than or equal to	(x is at most 4)
	Greater than or equal to	(y is at least 1)
	Not equal to	(5 is not equal to 3)

Try it now

Which symbol means 'greater than'?

Worked Examples

Is the statement true or false?

Identify the symbol

The symbol means 'greater than' → Reading: '8 is greater than 5'

Check the relationship

Is 8 larger than 5? Yes! → 8 is indeed larger

Determine truth value

Since 8 IS greater than 5, the statement is TRUE → TRUE

Answer: True. The statement correctly shows that 8 is greater than 5.

Common Mistakes

Confusing and symbols

Why it's wrong: The symbols look similar and it's easy to mix them up.

Correct: The symbol 'points to' the smaller value. Think of it as an alligator mouth that always wants to eat the bigger number: (mouth opens toward 5).

Thinking because

Why it's wrong: With negative numbers, the larger digit doesn't mean a larger value.

Correct: Use the number line: is further LEFT than , so . Think temperature: is colder than .

Confusing with 'less than'

Why it's wrong: Students forget the 'or equal to' part.

Correct: means 'less than OR equal to'. So is TRUE because 5 equals 5.

Interactive Visual

Range:to

Click on numbers to select them. Adjust the range to explore different values.

Interactive Sandbox

Expression Calculator

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Practice Problems

16 problems

Problem 1 of 16

Easy

Which symbol means 'greater than'?

Why It Matters

Inequalities describe real-world situations where things aren't exactly equal:

Speed limits: You must drive at most 50 km/h ()
Age requirements: You must be at least 18 to vote ()
Budget constraints: You can spend less than 100 euros ()
Temperature: It's warmer than yesterday ()

Unlike equations (which have one solution), inequalities often have many solutions!

Real World Applications

Speed Limits and Traffic Rules

Traffic laws use inequalities to set maximum and minimum speeds.

Example:

A highway speed limit of 120 km/h means your speed must satisfy .

1Try It Yourself

A school zone has a maximum speed of 30 km/h. A driver is going 35 km/h.

Is the driver breaking the speed limit? Write an inequality to show why.

Step 1: Write the mathematical expression

If speed must be at most 30, write the rule:

Shopping on a Budget

When shopping, you need to ensure your total stays within your budget.

Example:

If you have 50 euros, the total cost must satisfy .

2Try It Yourself

You have 40 euros and want to buy a book for 15 euros and a game.

What's the maximum price you can pay for the game?

Step 1: Write the mathematical expression

If book + game must be at most 40:

Key Takeaways

1Inequalities compare values using , , , , and
2The symbols and always 'point to' the smaller value
3On a number line, smaller values are to the LEFT
4 means 'less than OR equal to' and means 'greater than OR equal to'
5Unlike equations, inequalities can have many solutions

Frequently Asked Questions

means strictly less than (not equal), while includes equality. So is false, but is true.

Glossary

Inequality: A mathematical statement comparing two values that may not be equal, using symbols like , , ,
Less than (): A symbol showing that the left value is smaller than the right value
Greater than (): A symbol showing that the left value is larger than the right value
Less than or equal to (): A symbol meaning the left value is smaller than OR the same as the right value
Greater than or equal to (): A symbol meaning the left value is larger than OR the same as the right value
Solution set: All values that make an inequality true