Write an Inequality From a Constraint

1) Identify the quantity and the limit

A constraint describes a condition a number or expression must satisfy. First, decide what variable represents the unknown quantity. Then look for the key comparison words:

• at least / no less than / minimum means (\ge)
• more than / greater than means (>)
• at most / no more than / maximum means (\le)
• less than means (<)

2) Translate the words into symbols

Write the variable on the side that makes the sentence easy to read. Then place the inequality sign according to the wording.

Example pattern:

• “The number is at least 7” → (x \ge 7)
• “The cost is less than 20” → (c < 20)

3) Simplify the final expression

If the constraint includes arithmetic, compute it before finishing. For example, if a problem says “3 more than a number is at most 12,” write and simplify: (x + 3 \le 12). If possible, reduce the expression to a final clear form.

4) Check your inequality

Read it back in words to see whether it matches the original constraint. Also test a value that should work and a value that should not. If both fit the statement correctly, your inequality is likely right.