Of course! Let's solve each expression by
combining like terms. Like terms are terms that have the same variable raised to the same power. We add or subtract their coefficients.
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1. `2r + 1 + (-4r) + 7`
- Combine the `r` terms: `2r + (-4r) = -2r`
- Combine the constants: `1 + 7 = 8`
✔ Answer: `-2r + 8`
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2. `3z + 2 + (-5z) + 6`
- Combine the `z` terms: `3z + (-5z) = -2z`
- Combine the constants: `2 + 6 = 8`
✔ Answer: `-2z + 8`
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3. `-3z - z`
- This is the same as `-3z + (-1z)`
- Combine: `-3z - z = -4z`
✔ Answer: `-4z`
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4. `-4y - 4 + (-3)`
- The only variable term is `-4y`
- Combine constants: `-4 + (-3) = -7`
✔ Answer: `-4y - 7`
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5. `-2k + (-4k) + 5`
- Combine `k` terms: `-2k + (-4k) = -6k`
- Constant: `+5`
✔ Answer: `-6k + 5`
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6. `4t + 2 + (-3t) + 6`
- Combine `t` terms: `4t + (-3t) = t`
- Combine constants: `2 + 6 = 8`
✔ Answer: `t + 8`
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7. `4z - (-3z)`
- Subtracting a negative is adding: `4z + 3z = 7z`
✔ Answer: `7z`
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8. `-2k - (-5) + 1`
- Subtracting a negative becomes addition: `-2k + 5 + 1`
- Combine constants: `5 + 1 = 6`
✔ Answer: `-2k + 6`
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9. `-4q - (-8q) + 10`
- Subtracting a negative: `-4q + 8q + 10`
- Combine `q` terms: `4q`
✔ Answer: `4q + 10`
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10. `-4h + 3 + (-2h) + 3`
- Combine `h` terms: `-4h + (-2h) = -6h`
- Combine constants: `3 + 3 = 6`
✔ Answer: `-6h + 6`
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##
✔ Final Answers (in order):
1. `-2r + 8`
2. `-2z + 8`
3. `-4z`
4. `-4y - 7`
5. `-6k + 5`
6. `t + 8`
7. `7z`
8. `-2k + 6`
9. `4q + 10`
10. `-6h + 6`
Let me know if you’d like to see step-by-step work for any specific problem!
Parent Tip: Review the logic above to help your child master the concept of combining like terms algebra 1 worksheet.
