Two Steps
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 17 of 64.
In 2x + 3 < 11, two things happen to x. First x is multiplied by 2, then 3 is added. You solve it the same way as a two-step equation. Undo the addition first by subtracting 3 from both sides, then undo the multiplication by dividing both sides by 2:
2x < 8
x < 4
Subtracting 3 keeps the sign, and dividing by 2 keeps the sign because 2 is positive, so the < stays a < the whole way.
The order of the steps is the same as for equations. Undo the number that was added or subtracted first, and undo the coefficient last. To check the answer, try x = 0. It is less than 4, and 2 × 0 + 3 = 3, which is less than 11, so it satisfies the original inequality.
Challenge
EasySolve the inequality 3x + 5 > 20 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