Equations and inequalities · Ages 12–13

Equations and the balance worksheet

Part of: Linear equations in one unknown

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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.

1.5x + 33 = −7: take 33 from both sides, 5x = ; divide both by 5, x = .
Fill in each blank
Answer:
2.9x + 6 = 132: take 6 from both sides, 9x = ; divide both by 9, x = .
Fill in each blank
Answer:
3.15 − 2x = 11, x =
Answer:
4.x2 − 2 = 17, x =
Answer:
5.−2 − 5x = 8, x =
Answer:
6.5x + 5 = 30, x =
Answer:
7.7x + 26 = 41, x =
Answer in simplest form
Answer:
8.4x + 28 = 19, x =
Answer in simplest form
Answer:
9.9x + 24 = −30, x =
Answer:

13.6 pens and a $21 notebook: pay $200, get $119 change. How much is each pen?
Working:
Answer:
14.A tank holds 161 L and loses 13 L a minute. After how many minutes are 57 L left?
Working:
Answer:
15.Taxi: $22 to start, $3 a km, $37 in all. 3x + 22 = 37, 3x = , x = .
Fill in each blank
Working:
Answer:
16.A club: $150 to join, $60 a month, $330 paid so far. For how many months?
Working:
Answer:
17.112 sweets: keep 7 and share the rest among 7 friends. How many each?
Working:
Answer:
18.It is 1°C on the peak and falling 2°C an hour. After how many hours will it be −5°C?
Working:
Answer:

Show the answers and working

Equations and the balance worksheet: Answers and working

1. −40, −8
−7 − 33 = −40, −40 ÷ 5 = −8. Check with x = −8: 5x + 33 = −40 + 33 = −7.
2. 126, 14
132 − 6 = 126, 126 ÷ 9 = 14. Check with x = 14: 9x + 6 = 126 + 6 = 132.
3. 2
2x is what is taken away: 2x = 15 − 11 = 4, x = 2. Not 15 + 11.
4. 38
x2 = 17 + 2 = 19. Undo the division: x = 19 × 2 = 38.
5. −2
5x is what is taken away: 5x = −2 − 8 = −10, x = −2. Not −2 + 8.
6. 5
5 changes sign as it crosses: 5x = 30 − 5 = 25, then divide by 5: x = 5. When 30 is less than 5, 5x and x are both negative.
7. 157
7x = 15, so x = 157. A solution need not be whole: write it as a fraction in its lowest terms.
8. −94
4x = −9, so x = −94. A solution need not be whole: write it as a fraction in its lowest terms.
9. −6
24 changes sign as it crosses: 9x = −30 − 24 = −54, then divide by 9: x = −6. When −30 is less than 24, 9x and x are both negative.

10. True
Put in x = 10: 5 × 10 + 19 = 69. It is a solution only if that equals 69.
11. C. x = 3
2x + 1 = 7. Take 1 🧊 off each side: 2x = 6, so x = 3.
12. True
Put in x = 8: 9 × 8 + 16 = 88. It is a solution only if that equals 88.

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

13. 10 dollars
What was spent: 200 − 119 = 81. So 6x + 21 = 81, x = 10.
14. 8 minutes
161 − 13x = 57, 13x = 104, x = 8.
15. 15, 5
37 − 22 = 15, 15 ÷ 3 = 5, so 5 km.
16. 3 months
60x + 150 = 330. The joining fee is paid once, so x = (330 − 150) ÷ 60 = 3.
17. 15 sweets
7x + 7 = 112, 7x = 112 − 7, x = 15.
18. 3 hours
1 − 2x = −5, 2x = 1 + 5 = 6, x = 3. From 1 down to −5 is 1 + 5 degrees, not a difference.

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