Let's solve each expression by
combining like terms. Like terms are terms that have the same variable raised to the same power (or are constants). We'll simplify each expression step by step.
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1. $ 2r + 1 + (-4r) + 7 $
- Combine the $ r $-terms: $ 2r + (-4r) = -2r $
- Combine the constants: $ 1 + 7 = 8 $
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Answer: $ -2r + 8 $
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2. $ 3z + 2 + (-5z) + 6 $
- Combine $ z $-terms: $ 3z + (-5z) = -2z $
- Combine constants: $ 2 + 6 = 8 $
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Answer: $ -2z + 8 $
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3. $ -3z - z $
- Combine $ z $-terms: $ -3z - z = -4z $
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Answer: $ -4z $
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4. $ -4y - 4 + (-3) $
- Combine constants: $ -4 + (-3) = -7 $
- The $ y $-term remains: $ -4y $
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Answer: $ -4y - 7 $
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5. $ -2k + (-4k) + 5 $
- Combine $ k $-terms: $ -2k + (-4k) = -6k $
- Constant: $ +5 $
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Answer: $ -6k + 5 $
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6. $ 4t + 2 + (-3t) + 6 $
- Combine $ t $-terms: $ 4t + (-3t) = t $
- Combine constants: $ 2 + 6 = 8 $
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Answer: $ t + 8 $
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7. $ 4z - (-3z) $
- Subtracting a negative is adding: $ -(-3z) = +3z $
- So: $ 4z + 3z = 7z $
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Answer: $ 7z $
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8. $ -2k - (-5) + 1 $
- $ -(-5) = +5 $
- So: $ -2k + 5 + 1 = -2k + 6 $
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Answer: $ -2k + 6 $
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9. $ -4q - (-8q) + 10 $
- $ -(-8q) = +8q $
- So: $ -4q + 8q = 4q $
- Add constant: $ +10 $
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Answer: $ 4q + 10 $
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10. $ -4h + 3 + (-2h) + 3 $
- Combine $ h $-terms: $ -4h + (-2h) = -6h $
- Combine constants: $ 3 + 3 = 6 $
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Answer: $ -6h + 6 $
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✔ Final Answers:
| Expression | Simplified |
|----------|------------|
| $ 2r + 1 + (-4r) + 7 $ | $ -2r + 8 $ |
| $ 3z + 2 + (-5z) + 6 $ | $ -2z + 8 $ |
| $ -3z - z $ | $ -4z $ |
| $ -4y - 4 + (-3) $ | $ -4y - 7 $ |
| $ -2k + (-4k) + 5 $ | $ -6k + 5 $ |
| $ 4t + 2 + (-3t) + 6 $ | $ t + 8 $ |
| $ 4z - (-3z) $ | $ 7z $ |
| $ -2k - (-5) + 1 $ | $ -2k + 6 $ |
| $ -4q - (-8q) + 10 $ | $ 4q + 10 $ |
| $ -4h + 3 + (-2h) + 3 $ | $ -6h + 6 $ |
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🔍 Explanation:
To combine like terms:
- Identify variables and constants.
- Add or subtract coefficients of the same variable.
- Remember: subtracting a negative becomes addition.
- Keep the variable part unchanged.
This skill is foundational in algebra and helps simplify expressions before solving equations.
Parent Tip: Review the logic above to help your child master the concept of equivalent expressions worksheet.
