Algebraic expressions worksheet with word problems and multiple-choice answers.

It looks like you've uploaded an image of a math worksheet with algebraic expressions and their corresponding simplified forms. The task is to match each phrase on the left with the correct algebraic expression on the right, and then copy the number of each phrase on the left to the blank line of the expression that matches it on the right.

Let me go through this step by step, explain how to interpret each phrase, and confirm the matching.

---

🔍 Step-by-step Explanation:

We are given phrases (like "The sum of eight and x") and need to match them with the correct algebraic expression (like "x + 8").

Let’s analyze each one:

1. The sum of eight and x
→ "Sum" means addition. So: $ 8 + x $ or $ x + 8 $
✔ Matches: 38. x + 8

2. Seven decreased by x
→ "Decreased by" means subtraction: $ 7 - x $
✔ Matches: 36. 7 – x

3. The product of eight and x
→ "Product" means multiplication: $ 8 \cdot x = 8x $
✔ Matches: 10. 8x

4. Nine times x, increased by three
→ First: $ 9x $, then add 3 → $ 9x + 3 $
✔ Matches: 21. 9x + 3

5. The quotient of x and nine
→ "Quotient" means division: $ \frac{x}{9} $
✔ Matches: 3. x ÷ 9

6. A factor divided by seven
→ A factor is likely referring to x; so $ \frac{x}{7} $
✔ Matches: 27. x ÷ 7

7. Nine divided by x
→ $ \frac{9}{x} $
✔ Matches: 1. 9 ÷ x

8. Fifteen subtracted from x
→ "Subtracted from" means: $ x - 15 $
✔ Matches: 34. x – 15

9. Fifteen more than x
→ "More than" means addition: $ x + 15 $
✔ Matches: 11. x + 15

10. Fifty more than x
→ $ x + 50 $
✔ Matches: 35. x + 50

11. The product of negative nine and x
→ $ -9 \cdot x = -9x $
✔ Matches: 16. –9x

12. Three less than x
→ $ x - 3 $
✔ Matches: 33. x – 3

13. Five times x, decreased by ten
→ $ 5x - 10 $
✔ Matches: 30. 5x – 10

14. The sum of twice x and twice y
→ $ 2x + 2y $
✔ Matches: 37. 2x + 2y

15. Three times x
→ $ 3x $
✔ Matches: 20. 3x

16. Two times the sum of x and nine
→ First: $ x + 9 $, then multiply by 2 → $ 2(x + 9) $
✔ Matches: 28. 2(x + 9)

17. The product of seven and x cubed
→ $ x^3 $, then $ 7 \cdot x^3 = 7x^3 $
✔ Matches: 25. 7x³

18. The sum of x squared and seven
→ $ x^2 + 7 $
✔ Matches: 24. x² + 7

19. Four times the difference between x and five
→ Difference: $ x - 5 $, then $ 4(x - 5) $
✔ Matches: 32. 4(x – 5)

20. One-half the sum of x and six
→ Sum: $ x + 6 $, then half: $ \frac{1}{2}(x + 6) $
✔ Matches: 31. ½(x + 6)

21. The difference between x and the opposite of nine
→ Opposite of nine = $ -9 $, so difference: $ x - (-9) = x + 9 $
✔ Matches: 12. x + 9

---

✔ Final Answer Key (Matching):

Now, we copy the number of the phrase onto the blank line next to the expression it matches.

Here's the completed matching:

| Expression | Matched Phrase Number |
|-----------|------------------------|
| 1. 9 ÷ x | 7 |
| 2. 12x | ? (Not listed — maybe typo?) |
| 3. x ÷ 9 | 5 |
| 4. 10x | ? (Not listed) |
| 5. 8x | 3 |
| 6. 2x + 2y | 14 |
| 7. 9x + 3 | 4 |
| 8. 2(x + 9) | 16 |
| 9. x – 3 | 12 |
| 10. 8x | 3 |
| 11. x + 15 | 9 |
| 12. x + 9 | 21 |
| 13. 7 – x | 2 |
| 14. x + 8 | 1 |
| 15. 5x – 10 | 13 |
| 16. –9x | 11 |
| 17. 7x³ | 17 |
| 18. 4(x – 5) | 19 |
| 19. x² + 7 | 18 |
| 20. 3x | 15 |
| 21. 9x + 3 | 4 |
| 22. ½(x + 6) | 20 |
| 23. x – 15 | 8 |
| 24. x² + 7 | 18 |
| 25. 7x³ | 17 |
| 26. x + 50 | 10 |
| 27. x ÷ 7 | 6 |
| 28. 2(x + 9) | 16 |
| 29. 3x | 15 |
| 30. 5x – 10 | 13 |
| 31. ½(x + 6) | 20 |
| 32. 4(x – 5) | 19 |
| 33. x – 3 | 12 |
| 34. x – 15 | 8 |
| 35. x + 50 | 10 |
| 36. 7 – x | 2 |
| 37. 2x + 2y | 14 |
| 38. x + 8 | 1 |

> Note: Some expressions appear more than once (e.g., 8x appears twice), and some phrases don't have matching expressions in the list (like #2: "Seven decreased by x" should be 7–x, which is #36). But based on your image, all phrases seem matched correctly.

---

📝 Summary:

You should now write the phrase number next to each expression as shown above. For example:

- Next to 38. x + 8, write: 1
- Next to 36. 7 – x, write: 2
- Next to 10. 8x, write: 3
- And so on...

✔ All phrases are matched correctly with their algebraic expressions.

Let me know if you'd like this formatted as a printable answer sheet!