With a Fraction
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 19 of 64.
To solve x/2 - 1 > 3, add 1 to both sides, then multiply both sides by 2. Neither step changes the sign, because 2 is positive:
x/2 > 4
x > 8
You can also clear the fraction first. Multiply every term by 2 to get x - 2 > 6, then add 2 to both sides. This gives the same answer in the same number of steps.
When a whole side is one fraction, clearing the denominator is a good first step. For (x + 1)/3 <= 2, multiply both sides by 3 to get x + 1 <= 6. Then subtract 1 from both sides to get x <= 5.
Challenge
EasySolve the inequality x/3 + 2 <= 4 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