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TutorFinding the Unknown
  1. Why is x = 4?
  2. Think of x + 3 = 7 as a balance. Take 3 from both sides.x = 7 − 3 = 4
  3. Oh. I get it.

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TutorFinding the Unknown
Chapter 7

Why do we subtract 3 from both sides?

Tutor

Think of an equation as a balanced scale. Whatever you take away from one side, take away from the other.

x + 3 = 7
Same change. Both sides. Still balanced.

You’ll find this in section 7.2, Solving Equations Systematically, from page 168.

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NCERT
MathematicsGanita Prakash Part II
Grade 7
Contents
  1. 5Connecting the Dots...
  2. 6Constructions and Tilings
  3. 7Finding the Unknown
  • 7.1 Find the Unknowns164
  • 7.2 Solving Equations Systematically168
  • 7.3 Mind the Mistake, Mend the Mistake181
  • 7.4 A Pinch of History182

You’ll find this in section 7.2, page 168.

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Assessment GeneratorChapter 7, 20 marks
  • Multiple Choice
  • True / False
  • Fill in the Blank
  • Short Answer
  • Long Answer

Finding the Unknown

Mathematics

Time Allowed: 1 HourMaximum Marks: 20

Section A

(4 Marks)

Choose the correct option or fill in the blank.

  1. If x + 5 = 12, then x is
    • a)5
    • b)7
    • c)17
    • d)60
    (1)
  2. Which equation says “three times a number is 18”?
    • a)x + 3 = 18
    • b)3x = 18
    • c)x − 3 = 18
    • d)18x = 3
    (1)
  3. Adding 4 to only one side of an equation keeps it balanced.

    (True / False)

    (1)
  4. If 2x = 14, then x = ______.
    (1)

Section B

(6 Marks)

Answer in two or three steps.

  1. Solve 4x − 7 = 13 and check your answer.
    (2)
  2. Meena thinks of a number, doubles it and adds 9. She gets 25. Write an equation and find her number.
    (2)
  3. Ravi solved x − 6 = 10 and got x = 4. Find his mistake and correct it.
    (2)

Section C

(10 Marks)

  1. One pan of a balance holds 3 identical bags and a 4 kg weight. The other holds 19 kg. Write an equation and find the mass of one bag.

    OR

    The sum of three consecutive numbers is 48. Find the numbers.
    (1 × 5 = 5)
  2. Anu is 3 times as old as her brother. In 4 years, the sum of their ages will be 32. How old is each of them now?
    (5)

Finding the Unknown

Mathematics — Answer Key

Time Allowed: 1 HourMaximum Marks: 20

Section A

(4 Marks)

Choose the correct option or fill in the blank.

  1. If x + 5 = 12, then x is
    • a)5
    • b)7
    • c)17
    • d)60
    Ans. b. 7
    Explanation: Take 5 from both sides: 12 − 5 = 7.
    (1)
  2. Which equation says “three times a number is 18”?
    • a)x + 3 = 18
    • b)3x = 18
    • c)x − 3 = 18
    • d)18x = 3
    Ans. b. 3x = 18
    (1)
  3. Adding 4 to only one side of an equation keeps it balanced.

    (True / False)

    Ans. False
    Explanation: Whatever you do to one side, do to the other.
    (1)
  4. If 2x = 14, then x = ______.
    Ans. 7
    (1)

Section B

(6 Marks)

Answer in two or three steps.

  1. Solve 4x − 7 = 13 and check your answer.
    Ans. x = 5
    Explanation: Add 7 to both sides: 4x = 20. Divide by 4: x = 5. Check: 4 × 5 − 7 = 13.
    (2)
  2. Meena thinks of a number, doubles it and adds 9. She gets 25. Write an equation and find her number.
    Ans. 2x + 9 = 25, so x = 8
    (2)
  3. Ravi solved x − 6 = 10 and got x = 4. Find his mistake and correct it.
    Ans. x = 16
    Explanation: He took 6 away instead of adding it. Add 6 to both sides: x = 16.
    (2)

Section C

(10 Marks)

  1. One pan of a balance holds 3 identical bags and a 4 kg weight. The other holds 19 kg. Write an equation and find the mass of one bag.
    Ans. 3x + 4 = 19, so each bag is 5 kg

    OR

    The sum of three consecutive numbers is 48. Find the numbers.
    Ans. 15, 16 and 17
    Explanation: x + (x + 1) + (x + 2) = 48, so 3x + 3 = 48 and x = 15.
    (1 × 5 = 5)
  2. Anu is 3 times as old as her brother. In 4 years, the sum of their ages will be 32. How old is each of them now?
    Ans. Brother 6 years, Anu 18 years
    Explanation: x + 3x + 8 = 32, so 4x = 24 and x = 6.
    (5)
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