Multiply by a Positive
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 12 of 64.
x/2 > 3: half of x is more than 3, so x itself is more than 6. Multiplying both sides by 2 does it:
x > 6
Multiplying both sides by a positive number keeps the sign too. If 3 < 5, then 6 < 10: doubling both keeps the order.
As with equations, a fraction x/5 is undone by multiplying by 5, and 2x/3 by multiplying by 3 and then dividing by 2, or by multiplying by 3/2 in one go. Positive numbers, whichever way you do it, leave the sign alone.
Challenge
Solve 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