And versus Or

Part of the Inequalities & Absolute Value section of Coddy's Math journey. Lesson 39 of 64.

The two words are easy to mix up and the pictures keep them apart. x >= -3 and x < 1 is the overlap: the segment from -3 (included) to 1 (excluded), which is the chain -3 <= x < 1.

$x ≥ -3 and x < 1: the overlap, one segment$

x ≥ -3 and x < 1: the overlap, one segment

x < -3 or x >= 1 is everything outside that segment: two rays.

$x < -3 or x ≥ 1: two rays$

x < -3 or x ≥ 1: two rays

"And" narrows (both must hold, so fewer numbers qualify); "or" widens (either may hold, so more do).

Challenge

Show the solutions of x > -4 and x <= 2 on the number line.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This 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 Signs A Picture on a Line Closed or Open Reading It Backwards Recap: What an Inequality Is

4Two-Step Inequalities

Two Steps Subtract, Then Flip With a Fraction A Bracket on the Way Recap: Two-Step Inequalities

7Between Two Numbers

Two Conditions at Once Solving a Chain Two Moves on All Parts When the Chain Flips Chains with Fractions Recap: Between Two Numbers

10Absolute Value Inequalities

Less Than: Between Between, Shifted Greater Than: Outside Outside, Shifted Isolate, Then Split Always or Never Recap: Absolute Inequalities

2Adding and Subtracting

Add to Both Sides Subtract from Both Sides Negatives in the Mix Solve, Then Draw Recap: Adding and Subtracting

5Variables on Both Sides

x on Both Sides Gather Toward the Larger Brackets First Always True, Never True Recap: Variables on Both Sides

8One or the Other

Either Works Solving Each PartAnd versus OrRecap: One or the Other

11From Words to Inequalities

At Least, At Most More Than A Budget That Shrinks Two Limits Recap: From Words