Solving Inequalities and Representing on Number Lines
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Solving Inequalities and Representing on Number Lines — Free MYP3 Mathematics Practice Questions

1QuestionInterpreting Inequalities in Real-Life ScenariosConcept Practice
2 marks~3 minCriterion A
A rectangle has side lengths (x+3)(x + 3) cm and (x−1)(x - 1) cm. Its perimeter must be at least 20 cm.
a
Write an inequality to represent this condition and solve it for xx. [1]
b
Hence, calculate the smallest possible integer length of the shorter side, (x−1)(x - 1) cm. [1]
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Solutions

2QuestionSolving Two-Step InequalitiesAssessment Practice
3 marks~5 minCriterion C
The graph shows the line y=3x−7y = 3x - 7 and the horizontal line y=8y = 8. The two lines intersect at the point (5,8)(5, 8).
a
State what the intersection point (5,8)(5, 8) tells you about the equation 3x−7=83x - 7 = 8. [1]
b
Explain how the graph shows the solution to the inequality 3x−7≤83x - 7 \leq 8. [1]
c
Describe the complete solution set of 3x−7≤83x - 7 \leq 8 and justify why x=6x = 6 is not part of it. [1]
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Solutions

3QuestionInterpreting Inequalities in Real-Life ScenariosConcept Practice
2 marks~3 minCriterion B
The table below shows four real-life scenarios and their corresponding inequality symbols and circle types on a number line.

Scenario: "At least 5 people"symbol: ≥\geqcircle: closed
Scenario: "Fewer than 3 hours"symbol: <<circle: open
Scenario: "No more than 10 kg"symbol: ≤\leqcircle: closed
Scenario: "More than 2 km"symbol: >>circle: open
a
Describe the pattern that links the inequality symbol to the type of circle used. [1]
b
Apply this pattern to the scenario "Less than 7 dollars" and state the circle type required. [1]

Solutions

4QuestionGraphing Inequalities on a Number LineAssessment Practice
5 marks~8 minCriterion D
A student models a car's speed using the inequality v≤60v \leq 60 km/h, where vv is the speed in km/h. The number line below shows this model.

During the same time interval, the car's actual speed ranges from 55 km/h to 65 km/h.
a
Interpret what the inequality v≤60v \leq 60 km/h means in this context. [1]
b
Explain whether the inequality model accurately reflects the car's actual speed. [2]
c
Explain one limitation of using a single inequality to represent the car's speed. [2]
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Solutions

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