Inequality Keywords — Definition, Formula & Examples
Inequality keywords are everyday phrases in word problems—such as "at least," "at most," "no more than," and "fewer than"—that tell you which inequality symbol (, , , ) to use when writing a mathematical inequality.
Inequality keywords are verbal cues that map natural-language comparisons to the relational operators , , , and , enabling the translation of a word problem into an algebraic inequality.
How It Works
When you see a word problem, scan for comparison phrases and match each one to a symbol. "Greater than," "more than," and "above" translate to . "Less than," "fewer than," and "below" translate to . "At least," "no fewer than," and "minimum" translate to because the value can equal the boundary or exceed it. "At most," "no more than," and "maximum" translate to because the value can equal the boundary or fall below it. After choosing the correct symbol, place the variable expression on one side and the boundary value on the other.
Worked Example
Problem: A theater allows at most 200 people inside. Write an inequality for the number of people, p, allowed in the theater.
Identify the keyword: The phrase "at most" means the number can equal 200 or be less than 200.
Choose the symbol: "At most" translates to ≤.
Write the inequality: Place the variable on the left and the boundary on the right.
Answer:
Why It Matters
Standardized tests and algebra courses regularly present constraints as word problems. Recognizing these keywords quickly lets you set up the correct inequality on the first try, which is essential in topics like linear programming and systems of inequalities.
Common Mistakes
Mistake: Confusing "at least" with "less than" because both contain the word "least."
Correction: "At least 5" means 5 or more, so use , not . Think of it as the minimum acceptable value.