AQA · Mathematics · 8300
GCSE Maths: Inequalities on a number line
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Inequalities on a number line (Corbettmaths Video 177), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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On a number line representing an inequality, what does an open circle indicate?
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The value at that point is NOT included in the solution (< or >).
On a number line representing an inequality, what does a closed (filled) circle indicate?
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The value at that point IS included in the solution (≤ or ≥).
The inequality symbol for 'greater than or equal to' is ?
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≥
How do you solve the inequality 3x < 24?
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Divide both sides by 3 to get x < 8.
What is the first step to solve the inequality 3x − 8 > 16?
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Add 8 to both sides to get 3x > 24.
For the inequality 4 ≤ n < 8, what are all the integer values of n?
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4, 5, 6, 7
For the inequality −2 < n ≤ 3 where n is an integer, what are all possible values of n?
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−1, 0, 1, 2, 3
What is one integer that satisfies the inequality 6x > 42?
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Any integer greater than 7 (e.g., 8, 9, 10, etc.)
When solving the inequality 4n < 9 − 2n, what is the first step?
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Add 2n to both sides to get 6n < 9.
How do you solve the inequality 2(3x − 5) ≥ 43?
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Expand to get 6x − 10 ≥ 43, add 10 to get 6x ≥ 53, then divide by 6 to get x ≥ 53/6 (or x ≥ 8.83...).
For the compound inequality 3 < 2x + 1 < 13, what are all integer values of x?
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2, 3, 4, 5
What happens to the inequality sign when you multiply or divide both sides of an inequality by a negative number?
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The inequality sign reverses direction (< becomes >, ≤ becomes ≥, etc.).
If Annie spends m pounds, Beth spends twice as much, and Carly spends 5 pounds more than Annie, what inequality represents that their total spending is more than £60?
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m + 2m + (m + 5) > 60, which simplifies to 4m + 5 > 60
Annie spends m pounds, Beth spends 2m pounds, and Carly spends (m + 5) pounds. If 4m + 5 > 60, what is the minimum whole number value of m?
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m = 14. From 4m + 5 > 60, we get 4m > 55, so m > 13.75. The smallest whole number greater than 13.75 is 14.
When comparing perimeters of two shapes to form an inequality, what mathematical operation do you use?
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Set up an inequality comparing the two perimeter expressions. For example, if perimeter of shape A > perimeter of shape B, write the expression for A > expression for B.
What is the perimeter formula for a regular pentagon with side length s?
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5s (five times the side length, since all five sides are equal)
What is the perimeter formula for an isosceles triangle with two equal sides of length a and base b?
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2a + b (sum of the two equal sides plus the base)
Solve the inequality 8 < 10 − x/2 for x.
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x < 4. Subtract 10: −2 < −x/2. Multiply by −2 (reverse inequality): 4 > x, or x < 4.
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