A Flip on the Line
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 29 of 64.
When solving flips the sign, the direction of the shading flips too. To solve -2x < 6, divide both sides by -2 and flip the sign. The solution is x > -3. The shading goes to the right, even though the sign in the original inequality was <.
-2x < 6, that is x > -3: shaded to the right
The flip shows why you must solve before you draw. If you read the < in -2x < 6 as shade to the left, the picture is wrong. Solving gives x > -3, and that tells you to shade to the right.
Challenge
MediumShow the solutions of -3x > 9 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