L3 · Representing a situation with an inequality

Learning goal

“I can turn a real-world limit - a speed limit, a height restriction, a budget, a capacity - into an inequality with a defined variable, choosing strict or non-strict from the wording, and I can check a real value against it.”

Variable — a letter standing for the quantity that can vary (h for height in cm). Always define it: "let h = the rider's height in cm."

"At least" — the value or anything above it: at least 122 means 122 counts. Symbol: ≥.

"At most" — the value or anything below it: at most 48 means 48 counts. Symbol: ≤. ("No more than" means the same.)

"More than / less than" — strictly past the value: more than 16 means 16 itself is NOT enough. Symbols: > and <. ("Over", "under", "below", "fewer than" behave the same way.)

Worked example

"Riders must be at least 122 cm tall." Write the inequality. Step 1 (define): let h = a rider's height in cm. Step 2 (translate): "at least 122" means 122 is allowed and anything taller is allowed. Step 3 (choose the symbol): the boundary is included -> non-strict, pointing up -> h ≥ 122. Step 4 (check): a rider of exactly 122 cm: 122 ≥ 122, rides. A rider of 121 cm: 121 ≥ 122, does not. Say it plainly: the words decide the symbol. "At least / at most / no more than" include the boundary; "more than / less than / over / under" exclude it.

Check yourself — explain it

"At most 30 students" takes ≤ because...

Paired problem — example still visible

"A bus holds at most 48 passengers." Define a variable and write the inequality. -> p = number of passengers; p ≤ 48.

Faded completion — last step is yours

"'Tickets cost less than $20.' Let c = the ticket price in dollars. The boundary 20 is ______ (included/excluded), so the inequality is c ______ 20." -> excluded; < (c < 20)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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