Dividing by a Negative
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 14 of 64.
The sign flips whenever the coefficient of x is negative. In -x >= 4, the coefficient is -1. Divide both sides by -1 and flip the sign:
x <= -4
To solve -5x > -20, divide both sides by -5 and flip the sign. On the right, -20 divided by -5 is 4, because a negative divided by a negative is positive:
x < 4
Reverse the sign whenever you divide both sides by a negative number. It does not matter whether the number on the other side is positive or negative. Dividing by -5 reverses the sign in both -5x > 20 and -5x > -20.
Challenge
EasySolve 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