AQA · Mathematics · 8300
GCSE Maths: Inequalities: solving (one sign)
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Inequalities: solving (one sign) (Corbettmaths Video 178), 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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When solving an inequality, what operation reverses the inequality sign?
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Multiplying or dividing both sides by a negative number.
How do you represent x > 2 on a number line?
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Use an open circle at 2 and shade to the right. The open circle shows 2 is not included.
How do you represent x ≤ 4 on a number line?
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Use a closed (filled) circle at 4 and shade to the left. The closed circle shows 4 is included.
The inequality y ≥ 2 means y is greater than or equal to ?.
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2
What is the difference between a closed circle and an open circle on a number line for inequalities?
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A closed circle means the value is included (≤ or ≥). An open circle means the value is not included (< or >).
For the inequality 4 ≤ n < 8, which integers satisfy it?
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4, 5, 6, 7. The value 4 is included (≤) but 8 is not included (<).
To solve 3x < 24, what operation do you perform?
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Divide both sides by 3 to get x < 8. Since 3 is positive, the inequality sign does not reverse.
When solving 3x − 8 > 16, what are the steps?
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Add 8 to both sides to get 3x > 24, then divide by 3 to get x > 8.
For the inequality −2 < n ≤ 3 where n is an integer, what are the possible values of n?
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−1, 0, 1, 2, 3. The value −2 is not included (<) but 3 is included (≤).
What symbol represents 'greater than or equal to'?
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≥
When solving an inequality like 3x + 7 < 20, what is the first step?
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Isolate the variable term by subtracting 7 from both sides to get 3x < 13.
What is the solution to the inequality 3x + 7 < 20?
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x < 13/3 or x < 4.33...
When solving 9x + 4 < 5x − 14, what should you do after collecting like terms?
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Subtract 5x from both sides to get 4x + 4 < −14, then continue isolating x.
How do you find integer solutions to an inequality like −8 ≤ 2y < 0?
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First solve for y by dividing all parts by 2 to get −4 ≤ y < 0, then list all integers in that range: −4, −3, −2, −1.
If Lee is y years old and Toby is 8 years younger, and their combined age is less than 41, what inequality represents this?
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y + (y − 8) < 41 or 2y − 8 < 41
How do you solve a compound inequality like 3 < 2x + 1 < 13?
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Subtract 1 from all three parts to get 2 < 2x < 12, then divide all parts by 2 to get 1 < x < 6.
What are all integer solutions to 3 < 2x + 1 < 13?
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2, 3, 4, 5 (since 1 < x < 6 and x is an integer)
If Annie spends m pounds, Beth spends twice as much, and Carly spends 5 pounds more than Annie, and the total exceeds £60, what inequality represents this?
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m + 2m + (m + 5) > 60 or 4m + 5 > 60
When comparing perimeters to form an inequality, what must you do first?
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Calculate the expression for each perimeter, then set up an inequality comparing them.
When solving an inequality like 8 < 10 − x/2, what should you do after isolating the variable term?
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Rearrange to get −x/2 > −2, then multiply by −2 (remembering to reverse the inequality sign) to get x < 4.
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