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Closed or Open

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 3 of 64.

x >= 1 includes 1 itself: 1 is greater than or equal to 1. On the number line the dot at 1 is closed (filled in) to say so, and the shading runs right.

$x ≥ 1: a filled dot at 1, shaded to the right$

x ≥ 1: a filled dot at 1, shaded to the right

So the dot carries the difference between < and ≤: open for strict (<, >), closed for "or equal to" (≤, ≥). x <= -2 is a filled dot at -2 with shading to the left.

$x ≤ -2: a filled dot at -2, shaded to the left$

x ≤ -2: a filled dot at -2, shaded to the left

Challenge

Show the solutions of x <= 4 on the number line.

Try it yourself

x <= 4

Draw the graph

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Inequalities & Absolute Value

1What an Inequality Is

The Four Signs A Picture on a LineClosed or OpenReading It Backwards Recap: What an Inequality Is

4Two-Step Inequalities

Two Steps Subtract, Then Flip With a Fraction A Bracket on the Way Recap: Two-Step Inequalities

7Between Two Numbers

Two Conditions at Once Solving a Chain Two Moves on All Parts When the Chain Flips Chains with Fractions Recap: Between Two Numbers

10Absolute Value Inequalities

Less Than: Between Between, Shifted Greater Than: Outside Outside, Shifted Isolate, Then Split Always or Never Recap: Absolute Inequalities

2Adding and Subtracting

Add to Both Sides Subtract from Both Sides Negatives in the Mix Solve, Then Draw Recap: Adding and Subtracting

5Variables on Both Sides

x on Both Sides Gather Toward the Larger Brackets First Always True, Never True Recap: Variables on Both Sides

8One or the Other

Either Works Solving Each Part And versus Or Recap: One or the Other

11From Words to Inequalities

At Least, At Most More Than A Budget That Shrinks Two Limits Recap: From Words