Integer solutions
Objective. List integer values satisfying an inequality.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Listing integer solutions to an inequality means identifying all whole numbers that satisfy the given inequality within any stated range. After solving the inequality to find the range of values for the variable, pick out only the integers within that range, paying close attention to whether the boundary values are included or excluded. For example, if −3 < x ≤ 2, the integer solutions are −2, −1, 0, 1 and 2, since −3 itself is excluded by the strict inequality. When a question combines two inequalities, solve each separately first, then find the integers satisfying both conditions together.
Worked example
List all integer values of n that satisfy the inequality −2 ≤ n < 3.
- 1The inequality includes −2 since the left side uses ≤.
- 2The inequality excludes 3 since the right side uses a strict <.
- 3List the integers from −2 up to but not including 3.
- 4These integers are −2, −1, 0, 1, 2.
Answer: n = −2, −1, 0, 1, 2
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Practice
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Start practisingCommon mistake. Pupils often include a boundary value that should be excluded by a strict inequality sign, listing −3 in the solution set for −3 < x ≤ 2 when it should not appear. Check each inequality symbol carefully before listing values.
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