Solving Inequalities and Representing on Number Lines
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Solving Inequalities and Representing on Number Lines — Free MYP1 Mathematics Practice Questions

1QuestionInterpreting Inequalities in Real-Life ScenariosConcept Practice
2 marks~3 minCriterion D
Mia has between 10 dollars and 25 dollars to spend each week on snacks and a movie ticket. She writes the inequality 10≤amount<2510 \leq \text{amount} < 25 to model her spending.
a
Give an example of one real-life situation that can be shown using an inequality. [1]
b
Describe one reason why a simple inequality may not perfectly match real spending. [1]
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Solutions

2QuestionSolving One-Step InequalitiesAssessment Practice
6 marks~9 minCriterion B
A conjecture states: "Adding the same number to both sides of an inequality always keeps the inequality sign the same."
a
Identify whether each result is True or False. [2]

3<73 < 7, add 22: 5<9\quad 5 < 9

−2<5-2 < 5, add −3-3: −5<2\quad -5 < 2

4>−34 > -3, add −5-5: −1>−8\quad -1 > -8
b
State the general rule about what happens to an inequality when you add the same number to both sides. Use the word "preserves" in your answer. [2]
c
Describe how a number line shows why this rule works. [2]

Solutions

3QuestionUnderstanding Inequality SymbolsConcept Practice
2 marks~3 minCriterion C
A number line is shown with a closed circle at 33 and shading extending to the left.
a
Identify what the closed circle at 33 tells you about the number 33. [1]
b
State the inequality shown by the number line. [1]
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Solutions

4QuestionGraphing Inequalities on a Number LineConcept Practice
2 marks~3 minCriterion A
A school bus picks up students who live at least 5 km from school. Let dd be the distance, in kilometres, a student lives from school.
a
Identify what the inequality d≥5d \geq 5 means for a student wanting to use the bus. [1]
b
Describe why the value 5 km matters in deciding who can use the bus. [1]
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Solutions

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