A Flip on the Line
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 29 of 64.
When the algebra flips the sign, the picture flips its direction. -2x < 6 solves to x > -3 (divide by -2, flip): the shading runs to the right, even though the original sign pointed left.
-2x < 6, that is x > -3: shaded to the right
This is the clearest reason to solve before drawing. Read the original -2x < 6 as "shade left" and the picture is wrong. Solve it, and the answer x > -3 says exactly where to shade.
Challenge
Show 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