Let’s go through each expression one by one and combine like terms.
“Like terms” are terms that have the same variable (or no variable at all — those are just numbers). We add or subtract their coefficients.
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1. 5x + 3x - 2y
- Combine x terms: 5x + 3x = 8x
- The -2y has no other y term to combine with.
→
Answer: 8x - 2y
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2. -3a + 5b - 7b + a
- Combine a terms: -3a + a = -2a
- Combine b terms: 5b - 7b = -2b
→
Answer: -2a - 2b
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3. 8x - 2x + 3y + y
- Combine x terms: 8x - 2x = 6x
- Combine y terms: 3y + y = 4y
→
Answer: 6x + 4y
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4. 5 - 2m + 6m - 5
- Combine constants: 5 - 5 = 0
- Combine m terms: -2m + 6m = 4m
→
Answer: 4m
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5. 4s + 9s - 2t - 4t
- Combine s terms: 4s + 9s = 13s
- Combine t terms: -2t - 4t = -6t
→
Answer: 13s - 6t
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6. 9g + 3h - g - 2h
- Combine g terms: 9g - g = 8g
- Combine h terms: 3h - 2h = h
→
Answer: 8g + h
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7. -6x - 3y - 5x + 6y
- Combine x terms: -6x - 5x = -11x
- Combine y terms: -3y + 6y = 3y
→
Answer: -11x + 3y
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8. 3f + 9 - 1 - 7f
- Combine f terms: 3f - 7f = -4f
- Combine constants: 9 - 1 = 8
→
Answer: -4f + 8
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9. c - 4c + 8d + 2d
- Combine c terms: c - 4c = -3c
- Combine d terms: 8d + 2d = 10d
→
Answer: -3c + 10d
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10. 6x - y + 2x + 5y
- Combine x terms: 6x + 2x = 8x
- Combine y terms: -y + 5y = 4y
→
Answer: 8x + 4y
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11. 7x + 3y - 4z - 2y + 2x - 3x
- Combine x terms: 7x + 2x - 3x = 6x
- Combine y terms: 3y - 2y = y
- z term: -4z (no other z)
→
Answer: 6x + y - 4z
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12. 5m - 6n + 3p + m - 2p - p
- Combine m terms: 5m + m = 6m
- n term: -6n (only one)
- Combine p terms: 3p - 2p - p = 0p → disappears!
→
Answer: 6m - 6n
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Final Answer:
1. 8x - 2y
2. -2a - 2b
3. 6x + 4y
4. 4m
5. 13s - 6t
6. 8g + h
7. -11x + 3y
8. -4f + 8
9. -3c + 10d
10. 8x + 4y
11. 6x + y - 4z
12. 6m - 6n
Parent Tip: Review the logic above to help your child master the concept of combining like terms worksheet 7th grade.
