Negative Fractions
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 15 of 64.
-x/3 >= 2 hides two steps. Multiplying both sides by 3 first is a positive move, no flip: -x >= 6. Then dividing by -1 is a negative move, flip:
x <= -6
Alternatively, multiply both sides by -3 in one go: a negative move, so the sign flips once, and x <= -6 appears directly. Either way there is exactly one negative operation and exactly one flip.
Count the flips: each time you multiply or divide by a negative, the sign turns once. Two negative moves would turn it twice, back to where it began. Keeping count is easier than remembering the sign each time.
Challenge
Solve the inequality -x/4 < 1 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