Outside, Shifted
Part of the Inequalities & Absolute Value section of Coddy's Algebra journey. Lesson 51 of 64.
In |2x + 1| >= 5, the expression inside the bars is 2x + 1. Split into the two cases, then solve each case as a two-step inequality.
2x + 1 >= 5
2x >= 4
x >= 2
or
2x + 1 <= -5
2x <= -6
x <= -3
The solution is x <= -3 or x >= 2. On a number line, these are two rays pointing away from each other.
Solve each case with the ordinary inequality rules. If a case has a negative coefficient, flip the sign when you divide, as usual. Keep both cases to the end, and keep the word "or" between the two answers.
Challenge
MediumSolve the inequality |x - 3| > 1 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 Inequalities7Between Two Numbers
Two Conditions at OnceSolving a ChainTwo Moves on All PartsWhen the Chain FlipsChains with FractionsRecap: Between Two Numbers10Absolute Value Inequalities
Less Than: BetweenBetween, ShiftedGreater Than: OutsideOutside, ShiftedIsolate, Then SplitAlways or NeverRecap: Absolute 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