Equations and inequalities · Ages 12–13

Unknowns on both sides worksheet

Part of: Linear equations in one unknown

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Equations and inequalities · Ages 12–13

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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.

13.6 times a number minus 27 equals 3 times it plus 6. Put the steps of solving it in order.
- A. 3x = 33
- B. x = 11
- C. 6x − 27 = 3x + 6
- D. 6x − 3x = 6 + 27
Write the letters in the right order
Working:
Answer:
14.A square's sides: (7x − 8) cm and (5x + 10) cm. What is its perimeter?
Working:
Answer:
15.He runs 100 m/min; his brother, 180 m ahead, walks 70 m/min. Minutes to catch up?
Working:
Answer:
16.10 each is 6 short; 8 each leaves 16. 10x − 6 = 8x + 16, x = , sweets.
Fill in each blank
Working:
Answer:
17.A: $32, +$26 a week; B: $200, −$16 a week. Weeks until they match?
Working:
Answer:
18.A: $72 fee, $12 a book. B: $21 a book. 21x = 12x + 72, x = 72, x = .
Fill in each blank
Working:
Answer:

Show the answers and working

Unknowns on both sides worksheet: Answers and working

1. 4
Take 8x from both sides: 6x = 24, x = 4.
2. 3, −18, −6
6x − 3x = −11 − 7, that is 3x = −18, x = −6.
3. −3
Take 5x from both sides: 4x = −12, x = −3.
4. −4
Move the x terms right and the numbers left: −86 + 30 = 5x + 9x, so 14x = −86 + 30, x = −4.
5. 5
5x crosses to the left and −7 to the right, each changing sign: 8x − 5x = 8 + 7, 3x = 15, x = 5.
6. −116
6x = −11, so x = −116.
7. 73
9x = 21, so x = 73.
8. 8
6x crosses to the left and −32 to the right, each changing sign: 12x − 6x = 16 + 32, 6x = 48, x = 8.

9. True
13 becomes −13 as it crosses, so the right side is 17 − 13.
10. True
2 becomes −2 as it crosses, so the right side is 13 − 2.
11. A. 8x − 5x = 4 + 15
Each term changes sign as it crosses: 5x to −5x and −15 to +15.
12. B. 7x − 4x = 16 + 12
Each term changes sign as it crosses: 4x to −4x and −12 to +12.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. C → D → A → B
Form the equation, move the terms, collect them, then divide by 3.
14. 220 cm
A square's sides are equal: 7x − 8 = 5x + 10, x = 9. The side is 55 cm, the perimeter 220 cm. It asks the perimeter, not x.
15. 6 minutes
At the catch-up: 100x = 70x + 180. He gains 30 m a minute, so x = 6.
16. 11, 104
Both sides are the number of sweets. x = 11, and the sweets number 8 × 11 + 16 = 104.
17. 4 weeks
32 + 26x = 200 − 16x. One rises and one falls, so 26x + 16x = 200 − 32, 42x = 200 − 32, x = 4.
18. 9, 8
Each book saves $9, so 8 books make up the $72 membership.

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