Always or Never
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 53 of 64.
Because an absolute value is never negative, some of these inequalities settle themselves. |x| < -1 asks for a distance smaller than a negative number: impossible, no solution. |x - 4| > -2 asks for a distance greater than a negative number: true for every x, since every distance is at least 0.
These appear after isolating the bars too. |x + 2| + 3 < 1 becomes |x + 2| < -2: no solution. The sign of the number the bars are compared with decides everything, so isolate first and read that sign before splitting anything.
Challenge
Solve the inequality |x + 2| + 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