Either Works
Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 37 of 64.
"x is less than -2 or x is greater than 3" is a different kind of compound inequality. A number qualifies by satisfying either condition; it does not need both (and no number could). The solutions are two separate pieces of the number line, pointing away from each other:
x < -2 or x > 3: two rays, nothing between them
An "and" statement is one piece (the overlap of two conditions); an "or" statement is two pieces (everything either condition allows). The word is the whole difference, and the picture shows it at once: a segment for "and", two arrows for "or".
An "or" cannot be squeezed into a chain. x < -2 or x > 3 stays written as two inequalities joined by the word.
Challenge
Show the solutions of x <= -1 or x > 2 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 Solutions