Apply quadratic inequalities to real-world problems. Grade 11 Math 20-1 Alberta.
Lesson 2.9 of Linear Functions & Systems of Equations in Math 20-1 — Alberta curriculum lessons.
Why Vocabulary Matters. Before you can solve an inequality word problem, you need to translate the English sentence into a math statement. Every inequality symbol has one or more English phrases that signal it. Learn these phrases — they appear on every test.
Memory Tip — At Most vs At Least. At most = the highest it can be. The value can equal that amount, but cannot go higher. Use ≤.
At least = the lowest it can be. The value can equal that amount, but cannot go lower. Use ≥.
Students frequently mix these two up. Pause on every problem and ask: is the phrase setting a ceiling or a floor?
For each statement below, define a variable and write the corresponding inequality.
Part a) — All numbers less than 50. Define: Let x represent the number.
Key phrase: "less than" → strict inequality < (open boundary).
Inequality: x < 50
Part b) — The sum of two numbers exceeds 12. Define: Let x and y represent the two numbers.
Key phrase: "exceeds" means "greater than" → strict inequality >.
Inequality: x + y > 12
Part c) — A number decreased by 7 is at most 4. Define: Let x represent the number.
Parse the sentence: "decreased by 7" means subtract 7 from x, giving x - 7.
Key phrase: "at most 4" sets a ceiling → ≤ 4.
Inequality: x - 7 ≤ 4
Part d) — A number decreased by 5 is not more than another number increased by 2. Define: Let x and y represent the two numbers.
Key phrase: "not more than" → ≤ (same as "at most").
Left side: "a number decreased by 5" → x - 5
Right side: "another number increased by 2" → y + 2
Inequality: x - 5 ≤ y + 2
Create a free Studyio account to take the full lesson with voice-over teaching, practice questions and instant feedback.