Multiply by a Positive
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 12 of 64.
To solve x/2 > 3, multiply both sides by 2. Half of x is more than 3, so x itself is more than 6:
x > 6
Multiplying both sides of an inequality by a positive number keeps the sign as well. For example, 3 < 5 is true. Multiply both sides by 2 and you get 6 < 10, which is also true.
You undo a fraction the same way as in an equation. To undo x/5, multiply by 5. To undo 2x/3, multiply by 3 and then divide by 2, or multiply by 3/2 in one step. All of these numbers are positive, so the sign stays the same whichever way you do it.
Challenge
EasySolve the inequality x/5 <= 2 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