Unit 13 · Class 7 IB MYP · MCQ Test
Inequalities Introduction MCQ Test — Class 7 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Inequalities Introduction — MCQ Questions
1Which statement about inequality symbols is true?
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Answer: The symbol '>' means 'strictly greater than'.
Hint: Each symbol has a precise meaning. Consider what 'strictly' implies for a comparison.
Solution:
The symbol '<' means 'less than'.
The symbol '≥' means 'greater than or equal to'.
The symbol '>' means 'strictly greater than' (or simply 'greater than').
The symbol '≤' means 'less than or equal to'.
2The speed limit on a motorway in Germany is 130 km/h. If 's' represents the speed of a car, which inequality describes a car travelling at or below the speed limit?
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Answer: s ≤ 130
Hint: The phrase 'at or below' implies that the speed can be exactly 130 km/h or any value less than 130 km/h.
Solution:
The phrase 'at or below' means the speed 's' can be less than 130 OR equal to 130.
This combined condition is represented by the 'less than or equal to' symbol. — s ≤ 130
3Which description correctly represents the inequality x < 5 on a number line?
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Answer: An open circle at 5 with an arrow pointing to the left.
Hint: Remember that a strict inequality (like < or >) uses an open circle, while an inclusive inequality (like ≤ or ≥) uses a closed circle. The direction of the arrow indicates whether the values are greater or smaller.
Solution:
The inequality x < 5 means 'x is less than 5' and does not include 5 itself. Therefore, an open circle is used at the number 5.
Since x must be less than 5, the values are to the left of 5 on the number line.
4A number line shows a closed circle at -3 and an arrow pointing to the right. Which inequality does this represent?
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Answer: x ≥ -3
Hint: A closed circle indicates that the number itself is included in the solution. An arrow pointing to the right signifies values that are greater.
Solution:
A closed circle at -3 means that -3 is part of the solution, so it involves 'equal to'.
An arrow pointing to the right means the values are greater than -3.
Combining these, the inequality is 'x is greater than or equal to -3'. — x ≥ -3
5Solve the inequality: k + 7 > 15.
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Answer: k > 8
Hint: To isolate 'k', you need to perform the inverse operation of adding 7 to both sides of the inequality. Remember to keep the inequality sign the same.
Solution:
To solve for k, subtract 7 from both sides of the inequality. — k + 7 - 7 > 15 - 7
This simplifies to k > 8. — k > 8
6Solve the inequality: 4p ≤ 28.
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Answer: p ≤ 7
Hint: To isolate 'p', you need to divide both sides by 4. Since you are dividing by a positive number, the inequality sign remains unchanged.
Solution:
To solve for p, divide both sides of the inequality by 4. — 4p / 4 ≤ 28 / 4
This simplifies to p ≤ 7. — p ≤ 7
7Solve the inequality: 2m - 3 < 11.
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Answer: m < 7
Hint: Follow the same steps as solving a two-step equation: first, add or subtract to isolate the term with the variable, then multiply or divide.
Solution:
First, add 3 to both sides of the inequality. — 2m - 3 + 3 < 11 + 3 => 2m < 14
Next, divide both sides by 2 to solve for m. Since 2 is a positive number, the inequality sign does not change. — 2m / 2 < 14 / 2 => m < 7
8The minimum height for a roller coaster ride in an amusement park is 120 cm. If 'h' represents a person's height, which inequality describes the height required to ride?
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Answer: h ≥ 120
Hint: The word 'minimum' means the smallest acceptable value. Therefore, the height can be 120 cm or any value greater than 120 cm.
Solution:
The phrase 'minimum height' means the height 'h' must be at least 120 cm. This includes 120 cm itself and any height greater than 120 cm.
This condition is represented by the 'greater than or equal to' symbol. — h ≥ 120
9Alex solved the inequality -3x > 12 and stated the solution as x > -4. What mistake did Alex make?
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Answer: Alex forgot to reverse the inequality sign when dividing by a negative number.
Hint: Recall the special rule for inequalities: if you multiply or divide both sides by a negative number, you must flip the direction of the inequality sign.
Solution:
To solve -3x > 12, you must divide both sides by -3. — -3x / -3 > 12 / -3
When dividing (or multiplying) an inequality by a negative number, the inequality sign must be reversed. — x < -4
Alex correctly calculated 12 ÷ (-3) = -4, but incorrectly kept the '>' sign instead of flipping it to '<'.
10If the solution to an inequality is represented as x ≤ 6, which of these could be the original inequality?
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Answer: 2x ≤ 12
Hint: Solve each given inequality option and compare its solution to the target solution, x ≤ 6.
Solution:
Solve option A: x + 2 > 8 => x > 6. (Does not match)
Solve option B: 3x > 18 => x > 6. (Does not match)
Solve option C: x - 4 ≥ 2 => x ≥ 6. (Does not match)
Solve option D: 2x ≤ 12 => x ≤ 6. (Matches the given solution)
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Tips for Inequalities Introduction MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Inequalities Introduction MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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