Solving Inequalities and Representing on Number Lines
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Solving Inequalities and Representing on Number Lines — Free MYP2 Mathematics Practice Questions

1QuestionGraphing Inequalities on a Number LineConcept Practice
3 marks~5 minCriterion A
A number line has an open circle at −2-2 with shading extending to the right.
a
Identify the inequality shown by the number line. [1]
b
Explain what the open circle at −2-2 tells you about the values that satisfy the inequality. [1]
c
Compare the solution sets of x>−2x > -2 and x≥−2x \geq -2. State one way they are the same and one way they differ. [1]
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Solutions

2QuestionUnderstanding Inequality SymbolsAssessment Practice
6 marks~9 minCriterion C
A student solved −3<2x+1≤7-3 < 2x + 1 \leq 7 and drew a number line with an open circle at −2-2 and a closed circle at 33, but shaded the region outside the interval.

The student's algebraic steps were:

Step 1: −3<2x+1≤7-3 < 2x + 1 \leq 7
Step 2: −4<2x≤6-4 < 2x \leq 6
Step 3: −2<x≤3-2 < x \leq 3
a
Identify the error in the student's number line. [1]
b
Calculate the correct solution to −3<2x+1≤7-3 < 2x + 1 \leq 7, showing each algebraic step. [2]
c
Explain why each inequality symbol (<< or ≤\leq) stays the same throughout your working, and describe what the open and closed circles on your number line represent. [3]
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Solutions

3QuestionSolving One-Step InequalitiesConcept Practice
2 marks~3 minCriterion B
Each inequality below has the same solution, x<4x < 4.

x+3<7x+5<9x+2<6x+4<8x + 3 < 7 \quad x + 5 < 9 \quad x + 2 < 6 \quad x + 4 < 8
a
Identify the relationship between the number added to xx and the boundary point 4 in each inequality. [1]
b
Using this relationship, calculate the solution to x+6<10x + 6 < 10. [1]

Solutions

4QuestionGraphing Inequalities on a Number LineAssessment Practice
6 marks~9 minCriterion D
A city planner uses the inequality x≤5x \leq 5 to regulate the height (in metres) of new buildings near an airport.
a
State what the closed circle at x=5x = 5 means on a number line. [1]
b
Draw the inequality x≤5x \leq 5 on a number line scaled from 0 to 10. [2]
c
Identify one limitation of using a single inequality to control building heights, and explain how it could affect flight safety. [3]
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Solutions

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