MATHEMATICS - MULTI STEP EQUATIONS

Multi Step Equations Worksheet

  • 10 questions
  • Understand that a situation can be represented either in words or as an equation. Move between the two representations and solve the equation (integer coefficients, unknown on one side).
  • Difficulty: Hard
  • Board: CAIE
  • Attempt online on the examination portal

Here are the first 3 questions. Click “View all questions” to see the complete assessment.

Q1.

A storeroom had 4 identical cartons, each containing x notebooks. After 7 notebooks were given away, 37 remained. Which option gives the correct equation and value of x?

  1. A) 4x + 7 = 37, x = 7.5
  2. B) 4x − 7 = 37, x = 11
  3. C) 4(x − 7) = 37, x = 16.25
  4. D) 4x − 7 = 37, x = 7.5

Q2.

A number machine subtracts 4 from an input x and then doubles the result. Its output is 30. Which option correctly represents and solves this situation?

  1. A) 2(x − 4) = 30, x = 19
  2. B) 2x − 4 = 30, x = 17
  3. C) 2(x + 4) = 30, x = 11
  4. D) 2(x − 4) = 30, x = 11

Q3.

A rectangle has width x cm and length (x + 5) cm. Its perimeter is 50 cm. Which option gives the correct equation and width?

  1. A) 2x + 2(x + 5) = 50, x = 20 cm
  2. B) 2x + 2(x + 5) = 50, x = 10 cm
  3. C) x + (x + 5) = 50, x = 22.5 cm
  4. D) 4(x + 5) = 50, x = 7.5 cm

Q4.

Each of 5 shelves holds x books and 3 magazines. After 4 items are removed, 46 items remain. Which option correctly represents and solves the situation?

  1. A) 5x + 3 − 4 = 46, x = 9.4
  2. B) 5(x + 3) − 4 = 46, x = 7
  3. C) 5(x − 3) + 4 = 46, x = 11.4
  4. D) 5(x + 3) − 4 = 46, x = 5

Q5.

A bus initially has 6 rows with x students in each row. At one stop, 9 students leave and 3 students join. There are then 42 students. Which option is correct?

  1. A) 6x + 9 − 3 = 42, x = 6
  2. B) 6x − 9 + 3 = 42, x = 8
  3. C) 6(x − 9 + 3) = 42, x = 13
  4. D) 6x − 9 + 3 = 42, x = 6

Q6.

A taxi fare consists of a fixed charge of 7 dollars and 4 dollars for each kilometre travelled. A coupon reduces the fare by 6 dollars, and the final fare is 29 dollars. If x is the distance travelled, which option gives the correct equation and distance?

  1. A) 4x + 7 − 6 = 29, x = 7 km
  2. B) 7x + 4 − 6 = 29, x = 31/7 km
  3. C) 4x + 7 + 6 = 29, x = 4 km
  4. D) 4(x + 7) − 6 = 29, x = 1.75 km

Q7.

A rope is cut into 3 equal pieces, each originally x cm long. Then 2 cm is trimmed from every piece. The combined remaining length is 30 cm. Which option correctly represents and solves the situation?

  1. A) 3(x + 2) = 30, x = 8 cm
  2. B) 3(x − 2) = 30, x = 8 cm
  3. C) 3(x − 2) = 30, x = 12 cm
  4. D) 3x − 2 = 30, x = 32/3 cm

Q8.

A number x is reduced by 3. The result is multiplied by 4, and then 5 is added. The final result is 41. Which option gives the correct equation and value of x?

  1. A) 4x − 3 + 5 = 41, x = 9.75
  2. B) 4(x + 3) + 5 = 41, x = 6
  3. C) 4(x − 3) + 5 = 41, x = 12
  4. D) 4(x − 3) + 5 = 41, x = 9

Q9.

Study the balanced scale in the figure. Which option gives the equation represented by the scale and the mass of one bag?

Diagram for question 9: Study the balanced scale in the figure. Which option gives the equation represented by the scale and the…
  1. A) 3(x + 4) = 25, x = 13/3 kg
  2. B) 3x + 4 = 25, x = 7 kg
  3. C) 3x + 4 = 25, x = 9 kg
  4. D) 3x − 4 = 25, x = 29/3 kg

Q10.

The figure shows a rectangular garden. Which option gives the equation represented by the measurements and the garden's width?

Diagram for question 10: The figure shows a rectangular garden. Which option gives the equation represented by the measurements and…
  1. A) 2x + 2(x + 8) = 52, x = 9 m
  2. B) x + (x + 8) = 52, x = 22 m
  3. C) 4(x + 8) = 52, x = 5 m
  4. D) 2x + 2(x + 8) = 52, x = 11 m

What this assessment covers

Concepts Tested

  • multi step equations
  • Understand that a situation can be represented either in words or as an equation. Move between the two representations and solve the equation (integer coefficients, unknown on one side).

Question Mix

  • Hard questions included

Skills you build

  • Apply

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