Algebra
Single-variable inequalities
Writing inequalities
20 practice questions
2 video lessons
Theory + worked examples
Theory
An inequality compares two quantities. Translate the keywords:
- At least / no less than \(\to \ge\)
- At most / no more than \(\to \le\)
- More than / greater than \(\to >\)
- Less than / fewer than \(\to <\)
“At least” and “at most” include the value (\(\ge,\le\)); “more/less than” do not.
Comparison words to symbols.
\(x\ge3\) on a number line.
The four inequality symbols:
\[<,\quad >,\quad \le,\quad \ge\]
\(\le\) and \(\ge\) include equality; \(<\) and \(>\) do not.
How to write an inequality
- Identify the quantity and the comparison words.
- Decide if the boundary is included.
- Choose \(<,>,\le,\) or \(\ge\).
- Write the inequality.
Example 1 — At least
Write “a number \(x\) is at least \(5\)”.
Solution
“At least” includes \(5\).
| \(x\ge5\) |
Example 2 — Less than
Write “\(x\) is less than \(10\)”.
Solution
Strictly less, so \(<\).
| \(x<10\) |
Example 3 — No more than
Write “\(x\) is no more than \(20\)”.
Solution
“No more than” means at most.
| \(x\le20\) |
Example 4 — A budget
You have \(\$50\). Write an inequality for a cost \(c\) you can afford.
Solution
The cost can be up to \(50\).
| \(c\le50\) |
Common pitfalls
“At least” is \(\ge\), not \(>\).
“No more than” is \(\le\).
Include the boundary only for \(\le,\ge\).
Frequently asked questions
How do you write “at least 5”?
\(x\ge5\).
What symbol is “more than”?
\(>\), the strict greater-than.
Does “at most” include the number?
Yes — \(\le\) includes it.
What does \(\ge\) mean?
Greater than or equal to.
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