Loading...

About Inequalities Introduction — Class 7 IB

Represent and solve simple linear inequalities on number lines. This topic is part of the IB Class 7 mathematics syllabus (chapter: Unit 13). On this page you can practice 50 questions across three difficulty levels — 20 easy, 10 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 25-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Inequalities Introduction

  • Introduction to Inequalities: Beyond Equality
  • Decoding Inequality Symbols and Number Lines
  • Solving One-Step Inequalities
  • The 'Flip' Rule: Solving Two-Step Inequalities
  • Inequalities in Context: From Words to Math

Interactive lesson · about 15 minutes · checkpoint question after every unit

Inequalities Introduction — solved examples for Class 7 IB

Example 1easy

Which statement about inequality symbols is true?
  1. A)The symbol '<' means 'greater than or equal to'.
  2. B)The symbol '≥' means 'less than or equal to'.
  3. C)The symbol '>' means 'strictly greater than'.
  4. D)The symbol '≤' means 'not equal to'.

Step-by-step solution

  1. The symbol '<' means 'less than'.
  2. The symbol '≥' means 'greater than or equal to'.
  3. The symbol '>' means 'strictly greater than' (or simply 'greater than').
  4. The symbol '≤' means 'less than or equal to'.

Answer: The symbol '>' means 'strictly greater than'.

Example 2medium

The maximum number of passengers allowed on a bus in Copenhagen is 75. Let 'p' represent the number of passengers currently on the bus. Which inequality correctly represents this situation?
  1. A)p < 75
  2. B)p > 75
  3. C)p ≤ 75
  4. D)p ≥ 75

Step-by-step solution

  1. The term 'maximum' indicates that the number of passengers cannot exceed 75. This means the number of passengers can be 75 or any value less than 75.
  2. The inequality symbol that represents 'less than or equal to' is ≤.
  3. Therefore, if 'p' is the number of passengers, p ≤ 75 correctly represents the situation.

Answer: p ≤ 75

Example 3hard

If 'a' and 'b' are real numbers such that a < b, which of the following statements is **false**?
  1. A)A) a + 7 < b + 7
  2. B)B) -2a < -2b
  3. C)C) a / 3 < b / 3
  4. D)D) a - 10 < b - 10

Step-by-step solution

  1. Recall the fundamental properties of inequalities. Adding or subtracting the same number from both sides does not change the inequality sign.
  2. Multiplying or dividing by a positive number also does not change the inequality sign. So, options A, C, and D are true.
  3. However, when multiplying or dividing both sides of an inequality by a negative number, the inequality sign must be reversed. If a < b, then multiplying by -2 should result in -2a > -2b.
  4. Therefore, the statement -2a < -2b is false, as the sign was not reversed.

Answer: B) -2a < -2b

Practice questions on Inequalities Introduction

  1. Q1.easy

    The 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?
    1. A)s < 130
    2. B)s > 130
    3. C)s ≤ 130
    4. D)s ≥ 130
    Show answer

    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.

  2. Q2.easy

    Which description correctly represents the inequality x < 5 on a number line?
    1. A)A closed circle at 5 with an arrow pointing to the right.
    2. B)An open circle at 5 with an arrow pointing to the left.
    3. C)A closed circle at 5 with an arrow pointing to the left.
    4. D)An open circle at 5 with an arrow pointing to the right.
    Show answer

    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.

  3. Q3.easy

    A number line shows a closed circle at -3 and an arrow pointing to the right. Which inequality does this represent?
    1. A)x < -3
    2. B)x > -3
    3. C)x ≤ -3
    4. D)x ≥ -3
    Show answer

    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.

  4. Q4.medium

    A number line shows an open circle at -2, with the line shaded to the right. Which inequality does this number line represent?
    1. A)x ≤ -2
    2. B)x < -2
    3. C)x > -2
    4. D)x ≥ -2
    Show answer

    Answer: x > -2

    Hint: An open circle means the number itself is not included. Shading to the right indicates values greater than that number.

  5. Q5.medium

    Solve the inequality: m + 12 < 30
    1. A)m < 18
    2. B)m > 18
    3. C)m < 42
    4. D)m > 42
    Show answer

    Answer: m < 18

    Hint: To isolate 'm', you need to perform the inverse operation of adding 12 on both sides of the inequality.

  6. Q6.medium

    A botanist observes that a plant's height 'h' (in cm) must be at least 4 cm to survive. Which number line correctly represents the possible heights for the plant?
    1. A)A. An open circle at 4, shaded to the left.
    2. B)B. A closed circle at 4, shaded to the right.
    3. C)C. An open circle at 4, shaded to the right.
    4. D)D. A closed circle at 4, shaded to the left.
    Show answer

    Answer: B. A closed circle at 4, shaded to the right.

    Hint: The phrase 'at least' means the height can be 4 cm or greater. Think about whether 4 cm itself is included and which direction represents greater values.

  7. Q7.hard

    A group of students from Berlin are planning a cycling trip. They want to cycle at least 40 km each day but no more than 60 km. If they have already cycled 18 km by lunchtime, and they cycle at a steady speed of 14 km/h in the afternoon, what is the *largest integer* number of hours, 'h', they can cycle in the afternoon to meet their daily goal?
    1. A)A) 1 hour
    2. B)B) 2 hours
    3. C)C) 3 hours
    4. D)D) 4 hours
    Show answer

    Answer: C) 3 hours

    Hint: Set up two inequalities based on the minimum and maximum distance goals. Remember to find the common range for 'h' and then identify the largest integer within that range.

  8. Q8.hard

    Alex solved the inequality -3x + 7 > 19 as follows:
    Step 1: -3x > 19 - 7
    Step 2: -3x > 12
    Step 3: x > 12 / -3
    Step 4: x > -4
    Which step contains the first error in Alex's solution?
    1. A)A) Step 1
    2. B)B) Step 2
    3. C)C) Step 3
    4. D)D) Step 4
    Show answer

    Answer: D) Step 4

    Hint: Carefully review the rule for dividing by a negative number in inequalities. Does it affect the direction of the inequality sign?

  9. Q9.hard

    A number line shows an open circle at x = -3 and a closed circle at x = 5, with the line segment between them shaded. Which inequality best represents this number line?
    1. A)A) -3 < x < 5
    2. B)B) -3 ≤ x ≤ 5
    3. C)C) -3 < x ≤ 5
    4. D)D) -3 ≤ x < 5
    Show answer

    Answer: C) -3 < x ≤ 5

    Hint: Remember that an open circle indicates 'less than' or 'greater than' (strict inequality), while a closed circle indicates 'less than or equal to' or 'greater than or equal to' (inclusive inequality).

These are 9 of the 50 questions available for Inequalities Introduction. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.