Simplifying expressions worksheets | Worsheets library - Free Printable
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Step-by-step solution for: Simplifying expressions worksheets | Worsheets library
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying expressions worksheets | Worsheets library
Let's solve each expression by combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., $ 2x $ and $ 3x $, or $ 4y $ and $ -5y $). Constants (numbers without variables) can also be combined.
We'll go through each problem one by one.
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- Combine $ x $-terms: $ 2x + 3x = 5x $
- Combine constants: $ 7 - 2 + 3 = 8 $
- Answer: $ 5x + 8 $
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- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
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- $ 5x - x = 4x $
- Answer: $ 4x $
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- $ 5y + 7y = 12y $
- Answer: $ 12y $
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- $ y $-terms: $ 2y - 2y - 2y = -2y $
- Constants: $ 7 + 5 = 12 $
- Answer: $ -2y + 12 $
---
- $ x $-terms: $ 6x + x = 7x $
- Constants: $ 2 + 4 = 6 $
- Answer: $ 7x + 6 $
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- $ y $-terms: $ 5y + 9y = 14y $
- Constants: $ 4 + 6 = 10 $
- Answer: $ 14y + 10 $
---
- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
---
- $ y $-terms: $ y + 2y = 3y $
- Constants: $ 5 - 5 = 0 $
- Answer: $ 3y $
---
- $ y $-terms: $ 3y + 3y + 8y = 14y $
- Constants: $ 3 + 1 + 9 = 13 $
- Answer: $ 14y + 13 $
---
- $ x $-terms: $ x + 4x = 5x $
- Constants: $ 2 - 1 = 1 $
- Answer: $ 5x + 1 $
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- $ 8y + 4y = 12y $
- Answer: $ 12y $
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- $ y $-terms: $ 5y + 6y + 7y = 18y $
- Constants: $ 5 + 7 + 2 = 14 $
- Answer: $ 18y + 14 $
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- $ x $-terms: $ 2x + 7x = 9x $
- Constants: $ 8 - 7 = 1 $
- Answer: $ 9x + 1 $
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- $ y $-terms: $ -y + 2y = y $
- Constants: $ 6 + 6 + 6 + 3 = 21 $
- Answer: $ y + 21 $
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- $ y $-terms: $ 3y - y = 2y $
- Constant: $ 1 $
- Answer: $ 2y + 1 $
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- $ y $-terms: $ 7y - 4y = 3y $
- Constants: $ 1 + 6 = 7 $
- Answer: $ 3y + 7 $
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- $ 4y + y = 5y $
- Answer: $ 5y $
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- $ x $-terms: $ 14x - 8x = 6x $
- Constant: $ 9 $
- Answer: $ 6x + 9 $
---
- $ x $-terms: $ 16x - 4x - 7x = 5x $
- Constants: $ 13 - 11 = 2 $
- Answer: $ 5x + 2 $
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1. $ 5x + 8 $
2. $ 7x + 4 $
3. $ 4x $
4. $ 12y $
5. $ -2y + 12 $
6. $ 7x + 6 $
7. $ 14y + 10 $
8. $ 7x + 4 $
9. $ 3y $
10. $ 14y + 13 $
11. $ 5x + 1 $
12. $ 12y $
13. $ 18y + 14 $
14. $ 9x + 1 $
15. $ y + 21 $
16. $ 2y + 1 $
17. $ 3y + 7 $
18. $ 5y $
19. $ 6x + 9 $
20. $ 5x + 2 $
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To simplify expressions:
- Group like terms: variables with the same letter and exponent.
- Combine coefficients: add or subtract numbers in front of variables.
- Simplify constants: add or subtract all number terms.
- Always write the simplified expression in standard form (variables first, then constants).
Let me know if you'd like this formatted as a printable worksheet!
We'll go through each problem one by one.
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1. $ 2x + 7 + 3x - 2 + 3 $
- Combine $ x $-terms: $ 2x + 3x = 5x $
- Combine constants: $ 7 - 2 + 3 = 8 $
- Answer: $ 5x + 8 $
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2. $ 3x + 9 + 4x - 5 $
- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
---
3. $ 5x - x $
- $ 5x - x = 4x $
- Answer: $ 4x $
---
4. $ 5y + 7y $
- $ 5y + 7y = 12y $
- Answer: $ 12y $
---
5. $ 7 + 2y - 2y + 5 - 2y $
- $ y $-terms: $ 2y - 2y - 2y = -2y $
- Constants: $ 7 + 5 = 12 $
- Answer: $ -2y + 12 $
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6. $ 2 + 6x + 4 + x $
- $ x $-terms: $ 6x + x = 7x $
- Constants: $ 2 + 4 = 6 $
- Answer: $ 7x + 6 $
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7. $ 4 + 5y + 6 + 9y $
- $ y $-terms: $ 5y + 9y = 14y $
- Constants: $ 4 + 6 = 10 $
- Answer: $ 14y + 10 $
---
8. $ 3x + 9 + 4x - 5 $
- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
---
9. $ 5 + y - 5 + 2y $
- $ y $-terms: $ y + 2y = 3y $
- Constants: $ 5 - 5 = 0 $
- Answer: $ 3y $
---
10. $ 3y + 3 + 3y + 1 + 8y + 9 $
- $ y $-terms: $ 3y + 3y + 8y = 14y $
- Constants: $ 3 + 1 + 9 = 13 $
- Answer: $ 14y + 13 $
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11. $ 2 + x - 1 + 4x $
- $ x $-terms: $ x + 4x = 5x $
- Constants: $ 2 - 1 = 1 $
- Answer: $ 5x + 1 $
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12. $ 8y + 4y $
- $ 8y + 4y = 12y $
- Answer: $ 12y $
---
13. $ 5y + 5 + 6y + 7 + 7y + 2 $
- $ y $-terms: $ 5y + 6y + 7y = 18y $
- Constants: $ 5 + 7 + 2 = 14 $
- Answer: $ 18y + 14 $
---
14. $ 8 + 2x - 7 + 7x $
- $ x $-terms: $ 2x + 7x = 9x $
- Constants: $ 8 - 7 = 1 $
- Answer: $ 9x + 1 $
---
15. $ 6 + 6 - y + 6 + 2y + 3 $
- $ y $-terms: $ -y + 2y = y $
- Constants: $ 6 + 6 + 6 + 3 = 21 $
- Answer: $ y + 21 $
---
16. $ 1 + 3y - y $
- $ y $-terms: $ 3y - y = 2y $
- Constant: $ 1 $
- Answer: $ 2y + 1 $
---
17. $ 7y - 4y + 1 + 6 $
- $ y $-terms: $ 7y - 4y = 3y $
- Constants: $ 1 + 6 = 7 $
- Answer: $ 3y + 7 $
---
18. $ 4y + y $
- $ 4y + y = 5y $
- Answer: $ 5y $
---
19. $ 9 + 14x - 8x $
- $ x $-terms: $ 14x - 8x = 6x $
- Constant: $ 9 $
- Answer: $ 6x + 9 $
---
20. $ 16x - 4x - 7x + 13 - 11 $
- $ x $-terms: $ 16x - 4x - 7x = 5x $
- Constants: $ 13 - 11 = 2 $
- Answer: $ 5x + 2 $
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✔ Final Answers:
1. $ 5x + 8 $
2. $ 7x + 4 $
3. $ 4x $
4. $ 12y $
5. $ -2y + 12 $
6. $ 7x + 6 $
7. $ 14y + 10 $
8. $ 7x + 4 $
9. $ 3y $
10. $ 14y + 13 $
11. $ 5x + 1 $
12. $ 12y $
13. $ 18y + 14 $
14. $ 9x + 1 $
15. $ y + 21 $
16. $ 2y + 1 $
17. $ 3y + 7 $
18. $ 5y $
19. $ 6x + 9 $
20. $ 5x + 2 $
---
🔍 Explanation Summary:
To simplify expressions:
- Group like terms: variables with the same letter and exponent.
- Combine coefficients: add or subtract numbers in front of variables.
- Simplify constants: add or subtract all number terms.
- Always write the simplified expression in standard form (variables first, then constants).
Let me know if you'd like this formatted as a printable worksheet!
Parent Tip: Review the logic above to help your child master the concept of simplifying algebraic expressions worksheet.
