Inequalities: Show What’s Bigger (or Smaller!)

Lesson Plan - Get It!

Audio:

What Is an Inequality?

An inequality compares two values and shows that they are not equal.

Instead of using an equals sign (=), inequalities use symbols like these.

• | means greater than

• < means less than

• > means greater than or equal to

• < means less than or equal to

Here are some quick examples.

• 8 > 5 means 8 is greater than 5

• 3 < 10 means 3 is less than 10

• x > 4 means x can be 4 or any number bigger than 4

• y < 7 means y can be 7 or any number smaller than 7

Inequalities describe a whole range of possible answers, not just one.

Think in Ranges

Imagine this situation:

You have $20 to spend.

You cannot spend more than $20, so your spending amount (s) must follow this rule:

s < 20

That means:

You could spend $20, $15, $5, or even $0—but not $21.

Inequalities help describe limits like this in a clear way.

Visualize It: Number Lines

Numbers are easier to understand when you can see them.

A number line helps you show all the possible solutions to an inequality.

Here’s how to graph an inequality step by step.

1. Find the number in the inequality.

2. Draw a circle on that number.

3. Decide if the circle is open or closed.

   • Open circle: < or > (not included)

   • Closed circle: < or > (included)

4. Shade the direction that matches the inequality.

Example 1:

x < 1

This means x can be any number less than 1.

• Draw an open circle at 1.

• Shade everything to the left.

Example 2:

x > 2

This means x can be 2 or any greater value.

• Draw a closed circle at 2.

• Shade everything to the right.

Read the Graph Backward

You can also go the other way—turn a graph into an inequality.

Look at this step-by-step.

• Which direction is shaded?

  • Right means greater than.

  • Left means less than.

• Is the circle filled in?

  • Yes means include the number (> or <).

  • No means do not include it (> or <).

• What number is marked?

For example:

If the graph shows a closed circle at -3 and shading to the right, the inequality is:

x > -3

Why This Matters

Inequalities show up everywhere.

• Speed limits (you must drive < a certain speed)

• Game scores (you need > a certain number to win)

• Time limits (you must finish in < a certain time)

• Budgets (you can spend < what you have)

Instead of guessing, you can use inequalities to describe these limits clearly.

You’re Ready to Try It

You now know how to:

• Read and write inequalities.

• Understand what the symbols mean.

• Graph inequalities on a number line.

• Turn graphs back into inequalities.

Next, you’ll put these skills into action and test how well you can read, write, and graph inequalities on your own.