Divide by a Positive
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 11 of 64.
To solve 3x < 12, divide both sides by 3. Three copies of x add up to less than 12, so one copy is less than 4:
3x ÷ 3 < 12 ÷ 3
x < 4
Dividing both sides of an inequality by a positive number keeps the sign as it is. For example, 6 < 12 is true. Divide both sides by 3 and you get 2 < 4, which is also true. The smaller number is still the smaller number.
So far, you solve an inequality the same way you solve an equation. You can add a number to both sides, subtract a number from both sides, or divide both sides by a positive number, and the sign stays the same. Multiplying or dividing by a negative number works differently. It has its own lesson later in this chapter.
Challenge
EasySolve the inequality 4x < 28 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