Dividing by a Negative
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 14 of 64.
The flip appears whenever the coefficient of x is negative. -x >= 4 has coefficient -1: divide both sides by -1 and flip.
x <= -4
-5x > -20: divide by -5 and flip. Two negatives on the right make a positive 4.
x < 4
It is the operation that decides, not the numbers on the other side. Dividing by -5 flips; the -20 is just arithmetic. Read the coefficient of x, and if you are dividing by a negative, turn the sign around.
Challenge
Solve the inequality -4x > 8 for x.
Try it yourself
Solve for x
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