The Picture at the End
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 64 of 64.
A solution is only finished when you can see it. |x| > 2 is x < -2 or x > 2: two rays pointing away from each other, open dots at -2 and 2. An "and" would be a segment; an "or" is two pieces; a single inequality is one ray.
Whatever the algebra produced, the number line says it in one glance: where the dots are, whether they are filled, and which way the shading goes. Solve, then draw, and the two must agree.
Challenge
Solve |x - 1| >= 2 and show the solutions on the number line.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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 Solutions9Absolute Value Equations
Distance from ZeroThe Equation |x| = 3Distance from a PointIsolate the Bars FirstA Coefficient InsideNo Solution, One SolutionRecap: Absolute Equations12Final Challenges
Brackets and a FlipA Chain with a FlipA Wide Absolute ValueOutside, with a FractionThe Picture at the End