Simplifying expressions worksheets | Worsheets library - Free Printable
Educational worksheet: Simplifying expressions worksheets | Worsheets library. Download and print for classroom or home learning activities.
GIF
359×464
10 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1553735
⭐
Show Answer Key & Explanations
Step-by-step solution for: Simplifying expressions worksheets | Worsheets library
▼
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 constants (numbers without variables).
We'll go through each problem one by one.
---
- Combine $x$-terms: $2x + 3x = 5x$
- Combine constants: $7 - 2 + 3 = 8$
✔ Answer: $5x + 8$
---
- $x$-terms: $3x + 4x = 7x$
- Constants: $9 - 5 = 4$
✔ Answer: $7x + 4$
---
- $5x - x = 4x$
✔ Answer: $4x$
---
- $5y + 7y = 12y$
✔ Answer: $12y$
---
- $y$-terms: $2y - 2y - 2y = -2y$
- Constants: $7 + 5 = 12$
✔ Answer: $-2y + 12$
---
- $x$-terms: $6x + x = 7x$
- Constants: $2 + 4 = 6$
✔ Answer: $7x + 6$
---
- $y$-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: $5x + 1$
---
- $8y + 4y = 12y$
✔ Answer: $12y$
---
- $y$-terms: $5y + 6y + 7y = 18y$
- Constants: $5 + 7 + 2 = 14$
✔ Answer: $18y + 14$
---
- $x$-terms: $2x + 7x = 9x$
- Constants: $8 - 7 = 1$
✔ Answer: $9x + 1$
---
- $y$-terms: $-y + 2y = y$
- Constants: $6 + 6 + 6 + 3 = 21$
✔ Answer: $y + 21$
---
- $y$-terms: $3y - y = 2y$
- Constant: $1$
✔ Answer: $2y + 1$
---
- $y$-terms: $7y - 4y = 3y$
- Constants: $1 + 6 = 7$
✔ Answer: $3y + 7$
---
- $4y + y = 5y$
✔ Answer: $5y$
---
- $x$-terms: $14x - 8x = 6x$
- Constant: $9$
✔ Answer: $6x + 9$
---
- $x$-terms: $16x - 4x - 7x = 5x$
- Constants: $13 - 11 = 2$
✔ Answer: $5x + 2$
---
| Problem | Answer |
|--------|--------|
| 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 | $5x + 2$ |
---
To simplify algebraic expressions:
1. Identify like terms (same variables with same exponents).
2. Combine coefficients of like terms.
3. Combine constant terms.
4. Write the simplified expression in standard form (variables first, then constants).
This process is called combining like terms, a foundational skill in algebra.
Let me know if you'd like this as a printable PDF or need help with more problems!
We'll go through each problem one by one.
---
1. $ 2x + 7 + 3x - 2 + 3 $
- Combine $x$-terms: $2x + 3x = 5x$
- Combine constants: $7 - 2 + 3 = 8$
✔ Answer: $5x + 8$
---
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: $-2y + 12$
---
6. $ 2 + 6x + 4 + x $
- $x$-terms: $6x + x = 7x$
- Constants: $2 + 4 = 6$
✔ Answer: $7x + 6$
---
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: $14y + 13$
---
11. $ 2 + x - 1 + 4x $
- $x$-terms: $x + 4x = 5x$
- Constants: $2 - 1 = 1$
✔ Answer: $5x + 1$
---
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: $5x + 2$
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 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 algebraic expressions:
1. Identify like terms (same variables with same exponents).
2. Combine coefficients of like terms.
3. Combine constant terms.
4. Write the simplified expression in standard form (variables first, then constants).
This process is called combining like terms, a foundational skill in algebra.
Let me know if you'd like this as a printable PDF or need help with more problems!
Parent Tip: Review the logic above to help your child master the concept of simplifying algebraic expressions worksheet with answers.
