Subtract, Then Flip
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 18 of 64.
To solve 5 - 2x >= 1, subtract 5 from both sides. The sign stays the same, and you get -2x >= -4. Now the coefficient of x is -2. Divide both sides by -2 and flip the sign:
x <= 2
There are two steps, and one of them divides by a negative number, so the sign flips once. Check the answer with x = 0. It is at most 2, and 5 - 2 × 0 = 5, which is at least 1.
The sign flips at the step where you divide by the negative coefficient, not before. Subtracting 5 is an ordinary subtraction, and it leaves the sign alone. Ask two separate questions at each step: what are you undoing, and are you multiplying or dividing by a negative number?
Challenge
EasySolve 10 - 3x > 1.
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