Two Steps
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 17 of 64.
2x + 3 < 11 is built in two layers, like the two-step equations before: first x is doubled, then 3 is added. Undo the layers from the outside in: subtract 3, then divide by 2.
2x < 8
x < 4
Both moves are sign-safe (a subtraction and a division by a positive), so the < stays a < throughout.
The order is the same as for equations: the number that was added or subtracted last is undone first, and the coefficient is undone last. Check: 0 is below 4, and 2 × 0 + 3 = 3 is less than 11.
Challenge
Solve 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