Equations and inequalities · Ages 12–13
Equations with brackets worksheet
Part of: Linear equations in one unknown
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Equations with brackets worksheet
Equations and inequalities · Ages 12–13
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.7(x − 8) = 77, x =
Answer:
2.6(x + 5) = 0: opening up, 6x + = 0, so x = .
Fill in each blank
Answer:
3.8(x + 5) = 32: opening up, 8x + = 32, so x = .
Fill in each blank
Answer:
4.6 − 2(x − 9) = 14, x =
Answer:
5.−39 − 6(x − 4) = 15, x =
Answer:
6.2[3(x − 8) + 6] = 114, x =
Answer:
7.5(x − 28) = 9(x − 4), x =
Answer:
8.2[2(x − 2) + 7] = 94, x =
Answer:
Part B: Choose, or true or false (2 marks each)
9.4(x + 6) opens up to 4x + 24.
True or false?
Answer:
10.7(x + 9) opens up to 7x + 9.
True or false?
Answer:
11.Which is 35 − 7(x − 8) opened up correctly?
- A. 35 − 7x − 56
- B. 35 − 7x + 56
- C. 35 + 7x − 56
- D. 35 − 7x + 8
Choose the right answer
Answer:
12.Which is 27 − 3(x − 4) opened up correctly?
- A. 27 − 3x − 12
- B. 27 + 3x − 12
- C. 27 − 3x + 12
- D. 27 − 3x + 4
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Three consecutive even numbers add up to 174. What is the largest of them?
Working:
Answer:
14.6 friends: a ticket and a $21 popcorn each, $654 in all. How much is a ticket?
Working:
Answer:
15.4 h at x km/h, then 3 h at 10 km/h faster: 450 km in all. What is x?
Working:
Answer:
16.Trapezium: area 51 cm², height 6 cm, one base 11 cm. How long is the other?
Working:
Answer:
17.Put the steps of solving 7(x − 7) = 5(x + 1) in order.
- A. 7(x − 7) = 5(x + 1)
- B. 2x = 54
- C. 7x − 49 = 5x + 5
- D. x = 27
Write the letters in the right order
Working:
Answer:
18.Length = width + 8 cm; perimeter 56 cm. 2(x + x + 8) = 56, 2x + 8 = , x = .
Fill in each blank
Working:
Answer:
Show the answers and working
Equations with brackets worksheet: Answers and working
Part A: Working out and filling in
1. 19
Treat the bracket as one thing: x − 8 = 77 ÷ 7 = 11, x = 19.
2. 30, −5
6 × 5 = 30; 6x = 0 − 30 = −30, x = −5. Or divide both sides by 6 first.
3. 40, −1
8 × 5 = 40; 8x = 32 − 40 = −8, x = −1. Or divide both sides by 8 first.
4. 5
A minus in front of the bracket: 6 − 2x + 18 = 14. So 2x = 6 + 18 − 14, x = 5.
5. −5
A minus in front of the bracket: −39 − 6x + 24 = 15. So 6x = −39 + 24 − 15, x = −5.
6. 25
Peel from outside in: 3(x − 8) + 6 = 57, 3(x − 8) = 51, x − 8 = 17, x = 25.
7. −26
Open up: 5x − 140 = 9x − 36. Move terms: −140 + 36 = 9x − 5x, so 4x = −104, x = −26.
8. 22
Peel from outside in: 2(x − 2) + 7 = 47, 2(x − 2) = 40, x − 2 = 20, x = 22.
Part B: Choose, or true or false
9. True
The 4 outside multiplies every term inside: 4 × 6 = 24.
10. False
The 7 outside multiplies every term inside: 7 × 9 = 63.
11. B. 35 − 7x + 56
−7 times x is −7x, and −7 times −8 is +56.
12. C. 27 − 3x + 12
−3 times x is −3x, and −3 times −4 is +12.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 60
Consecutive evens differ by 2: x + (x + 2) + (x + 4) = 174, x = 56. The largest is 60.
14. 88 dollars
6(x + 21) = 654, x + 21 = 109, x = 88. Don't take 21 off just once.
15. 60 km/h
4x + 3(x + 10) = 450. Collecting, 7x + 30 = 450, x = 60.
16. 6 cm
(x + 11) × 6 ÷ 2 = 51, so x + 11 = 17, x = 6.
17. A → C → B → D
Open the brackets, move and collect the terms, then divide by 2.
18. 28, 10
Divide both by 2: 2x + 8 = 28, x = 10. A perimeter is twice length plus width.
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