Let’s go through each problem 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 (the numbers in front) and keep the variable part the same.
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Problem 1: 6k + 2 – 4k
- Like terms with k: 6k and –4k → 6k – 4k =
2k
- Constant term:
+2
→ Final:
2k + 2
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Problem 2: –8h – 5 – 9h
- Like terms with h: –8h and –9h → –8h – 9h =
–17h
- Constant term:
–5
→ Final:
–17h – 5
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Problem 3: –6f + 3 + 10f
- Like terms with f: –6f and 10f → –6f + 10f =
4f
- Constant term:
+3
→ Final:
4f + 3
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Problem 4: –7x + x + 2x
- All terms have x: –7x + 1x + 2x → (–7 + 1 + 2)x =
–4x
→ Final:
–4x
*(Note: “x” means “1x”)*
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Problem 5: 20w – 3 – 5w + 7
- Like terms with w: 20w – 5w =
15w
- Constants: –3 + 7 =
+4
→ Final:
15w + 4
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Problem 6: –5 – 4y + 10y
- Like terms with y: –4y + 10y =
6y
- Constant:
–5
→ Final:
6y – 5
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Problem 7: –4 + 6z² – 3 + 5z²
- Like terms with z²: 6z² + 5z² =
11z²
- Constants: –4 – 3 =
–7
→ Final:
11z² – 7
*(Note: z² is a different term than z, so we don’t mix them. Here, only z² terms and constants.)*
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Problem 8: 7n – 9 – 3 – 9n
- Like terms with n: 7n – 9n =
–2n
- Constants: –9 – 3 =
–12
→ Final:
–2n – 12
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Problem 9: 18p – 6 – 7p
- Like terms with p: 18p – 7p =
11p
- Constant:
–6
→ Final:
11p – 6
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Problem 10: –2 + 4q + 8 – 9q
- Like terms with q: 4q – 9q =
–5q
- Constants: –2 + 8 =
+6
→ Final:
–5q + 6
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Final Answer:
1. 2k + 2
2. –17h – 5
3. 4f + 3
4. –4x
5. 15w + 4
6. 6y – 5
7. 11z² – 7
8. –2n – 12
9. 11p – 6
10. –5q + 6
Parent Tip: Review the logic above to help your child master the concept of simplifying expressions by combining like terms worksheet.
![Combining Like Terms Worksheets [PDF] (7.EE.A.1): 7th Grade Math](/images2/simplifying-expressions-by-combining-like-terms-worksheet/simplifying-expressions-by-combining-like-terms-worksheet-21.png)
