Closed or Open
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 3 of 64.
The solutions of x >= 1 include 1 itself, because 1 is greater than or equal to 1. On the number line, the dot at 1 is closed (filled in) to show that 1 is a solution. The shading runs to the right.
x ≥ 1: a filled dot at 1, shaded to the right
The dot shows the difference between < and ≤. It is open for a strict sign (< or >) and closed for a sign with "or equal to" (≤ or ≥). For example, x <= -2 is a filled dot at -2 with shading to the left.
x ≤ -2: a filled dot at -2, shaded to the left
Challenge
EasyShow the solutions of x <= 4 on the number line.
Try it yourself
Draw the graph
Test yourselfThis 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 SignsA Picture on a LineClosed or OpenReading It BackwardsRecap: What an Inequality Is4Two-Step Inequalities
Two StepsSubtract, Then FlipWith a FractionA Bracket on the WayRecap: Two-Step Inequalities2Adding and Subtracting
Add to Both SidesSubtract from Both SidesNegatives in the MixSolve, Then DrawRecap: Adding and Subtracting5Variables on Both Sides
x on Both SidesGather Toward the LargerBrackets FirstAlways True, Never TrueRecap: Variables on Both Sides11From Words to Inequalities
At Least, At MostMore ThanA Budget That ShrinksTwo LimitsRecap: From Words3Multiplying and Dividing
Divide by a PositiveMultiply by a PositiveThe FlipDividing by a NegativeNegative FractionsRecap: Multiply and Divide6Graphing Solutions
From Inequality to PictureIs the Endpoint In?A Flip on the LineRecap: Graphing Solutions