Algebra and equations · Ages 11–12
Equations with brackets and like terms worksheet
Part of: Equations with brackets, decimals and fractions
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Equations with brackets and like terms worksheet
Algebra and equations · Ages 11–12
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.Solve 7x + 6x = 169. x =
Answer:
2.Solve 2(x + 1) = 8. x =
Answer:
3.Solve 12x − 8x = 13. x =
Answer:
4.Solve 5(x − 2) = 12.5. x =
Answer:
5.Solve 4(x − 7) = 10. x =
Answer:
6.Solve 7x − 5x = 39. x =
Answer:
7.Solve 2x + 2x + 21 = 81. x =
Answer:
8.Solve 4x + 5x + 1 = 19. x =
Answer:
Part B: Choose, or true or false (2 marks each)
9.Solving 9(x + 5) = 81, which step is right?
- A. Divide both sides by 9: x + 5 = 9
- B. Take 5 from both sides: 9x = 76
- C. Multiply both sides by 9: x + 5 = 729
- D. Take 9 from both sides: x + 5 = 72
Choose the right answer
Answer:
10.Solving 3(x + 9) = 42, which step is right?
- A. Take 3 from both sides: x + 9 = 39
- B. Multiply both sides by 3: x + 9 = 126
- C. Take 9 from both sides: 3x = 33
- D. Divide both sides by 3: x + 9 = 14
Choose the right answer
Answer:
11.x = 7 solves 2(x + 9) = 32.
True or false?
Answer:
12.x = 12 solves 4(x + 5) = 68.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.3 children each buy a meal of a $22 burger and a drink, paying $108 in all. How much is each drink?
Working:
Answer:
14.Ka-yee and Ka-lok have 133 stickers between them. Ka-yee has 23 more than 4 times as many as Ka-lok. How many stickers does Ka-lok have?
Working:
Answer:
15.Chi-keung has 5 times as many stamps as Ka-yee, which is 64 more stamps than Ka-yee. How many stamps does Ka-yee have?
Working:
Answer:
16.Ka-lok buys 2 boxes of chocolates on Saturday and 3 more of the same boxes on Sunday, paying $55 in all. How much is each box?
Working:
Answer:
17.Three whole numbers in a row add up to 216. What is the smallest?
Working:
Answer:
18.7 children each buy a meal of a $26 burger and a drink, paying $238 in all. How much is each drink?
Working:
Answer:
Show the answers and working
Equations with brackets and like terms worksheet: Answers and working
Part A: Working out and filling in
1. 13
7x and 6x are like terms, so join them into one first.
Join the like terms: 13x = 169, so x = 169 ÷ 13 = 13.
2. 3
2 multiplies the whole bracket, so divide both sides by 2 first.
Divide both sides by 2: x + 1 = 4; take 1 from both sides: x = 3.
3. 3.25
12x − 8x are like terms, so first work out how many x are left.
Join the like terms: 4x = 13, so x = 13 ÷ 4 = 3.25.
4. 4.5
5 multiplies the whole bracket, so divide both sides by 5 first and see what x − 2 is.
Divide both sides by 5: x − 2 = 2.5; add 2 to both sides: x = 4.5.
5. 9.5
4 multiplies the whole bracket, so divide both sides by 4 first and see what x − 7 is.
Divide both sides by 4: x − 7 = 2.5; add 7 to both sides: x = 9.5.
6. 19.5
7x − 5x are like terms, so first work out how many x are left.
Join the like terms: 2x = 39, so x = 39 ÷ 2 = 19.5.
7. 15
Join 2x and 2x first, then take 21 from both sides.
Join: 4x + 21 = 81; take 21 from both sides: 4x = 60; x = 15.
8. 2
Join 4x and 5x first, then take 1 from both sides.
Join: 9x + 1 = 19; take 1 from both sides: 9x = 18; x = 2.
Part B: Choose, or true or false
9. A. Divide both sides by 9: x + 5 = 9
9 multiplies the whole bracket, not just x. Which step deals with the bracket as a whole?
9 multiplies the whole bracket, so divide both sides by 9: x + 5 = 9, x = 4.
10. D. Divide both sides by 3: x + 9 = 14
3 multiplies the whole bracket, not just x. Which step deals with the bracket as a whole?
3 multiplies the whole bracket, so divide both sides by 3: x + 9 = 14, x = 5.
11. True
Put x = 7 into 2(x + 9) and see whether it comes to 32.
Check by putting it in: with x = 7, 2 × (7 + 9) = 32, so the answer is x = 7.
12. True
Put x = 12 into 4(x + 5) and see whether it comes to 68.
Check by putting it in: with x = 12, 4 × (12 + 5) = 68, so the answer is x = 12.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 14 dollars
Let a drink be $x: each meal is x + 22, and 3 of them make 108: 3(x + 22) = 108.
Let a drink be $x: 3(x + 22) = 108; x + 22 = 36; x = 14.
14. 22 stickers
Let Ka-lok have x, so Ka-yee has 4x + 23. Together they make 133.
Let Ka-lok have x, so Ka-yee has 4x + 23: x + 4x + 23 = 133, 5x = 110, x = 22.
15. 16 stamps
Let Ka-yee have x, so Chi-keung has 5x. How many more x does Chi-keung have than Ka-yee?
Let Ka-yee have x: 5x − x = 64, 4x = 64, x = 16.
16. 11 dollars
Let a box be $x: the two days are 2x + 3x. Join the like terms first.
Let a box be $x: 2x + 3x = 55, 5x = 55, x = 11.
17. 71
Let the smallest be x, so the three are x, x + 1 and x + 2. Add them up.
Let the smallest be x, so the three are x, x + 1, x + 2: 3x + 3 = 216, 3x = 213, x = 71 (71, 72, 73).
18. 8 dollars
Let a drink be $x: each meal is x + 26, and 7 of them make 238: 7(x + 26) = 238.
Let a drink be $x: 7(x + 26) = 238; x + 26 = 34; x = 8.
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