Inequalities Are Regions

Lesson 5 of 12 · 7 min · Free, no account needed

What you will learn

An inequality like h > 140 has many solutions: a whole region of the number line, its solution set.
An open dot means the boundary is not included (> or <); a filled dot means it is (≥ or ≤).
Solve it like an equation, but multiply or divide by a negative and the sign flips.
With two variables, y > 2x + 1 is a half-plane: everything above a line.

To ride the coaster you must be taller than 140 cm. Who can ride?
Tap every kid who gets on.
Paint every height that can ride.
Drag the dot to the boundary. Tap it: open means the boundary itself is out. Then drag along the line to paint.
What happens to x > 3 if you multiply both sides by −1?
Press Step and watch the line.
An inequality is a region.
An inequality compares with >, <, ≥ or ≤. Its solutions fill a whole region: the solution set.
Open dot: the boundary is not included (> or <). Filled dot: it is (≥ or ≤).
Solve like an equation: −2x > 6. Divide both sides by −2, and because −2 is negative, the sign flips: x < −3.
Paint where −2x > 6.
Divide both sides by −2 first. Mind the sign. The test numbers light up inside your region.
Game: region hunter.
Paint each region and lock it in. A streak multiplies your points.
Open your own ride.
Build the height rule for your ride from a sign and a number. Check opens the gate.
An AI calls an animal a dog when y > 2x + 1. Which points are dogs?
x and y are two measurements of each animal. Tap every point the model calls a dog.
A crowd of 30 kids comes to your ride. How many get on?
Your rule is on the sign. Drag the marker to your guess, then Check.

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