Algebraic Expressions 6 Worksheets - Free Printable

Explanation:
We need to translate each English phrase into an algebraic expression. Let’s go one by one, using x to represent “a number” (unless another variable is needed — but here, all refer to the same unknown number, so we’ll use x consistently).

1. *A number squared is equal to one-thousand nine-hundred thirty-six.*
→ “A number squared” = $ x^2 $
→ “is equal to 1936” → $ x^2 = 1936 $

2. *A number decreased by twenty is equal to zero.*
→ “A number decreased by twenty” = $ x - 20 $
→ equals zero → $ x - 20 = 0 $

3. *The product of a number and eight squared is equal to eighty-eight.*
→ “eight squared” = $ 8^2 = 64 $
→ “product of a number and 64” = $ x \cdot 64 $ or $ 64x $
→ equals 88 → $ 64x = 88 $

4. *A number cubed is equal to 64.*
→ “a number cubed” = $ x^3 $
→ equals 64 → $ x^3 = 64 $

5. *The difference of a number and twelve is thirty-six.*
→ “difference of a number and twelve” = $ x - 12 $
→ equals 36 → $ x - 12 = 36 $

6. *Eight more than a number is 22.*
→ “eight more than a number” = $ x + 8 $
→ equals 22 → $ x + 8 = 22 $

7. *The product of minus twelve and a number is twenty-six.*
→ “minus twelve” = $ -12 $
→ product with a number = $ -12 \cdot x = -12x $
→ equals 26 → $ -12x = 26 $

8. *The sum of minus twelve and a number is equal to twenty-two.*
→ “sum of minus twelve and a number” = $ -12 + x $ or $ x - 12 $
→ equals 22 → $ x - 12 = 22 $

9. *A number plus four times that number is equal to 44.*
→ “a number” = $ x $
→ “four times that number” = $ 4x $
→ sum = $ x + 4x = 5x $
→ equals 44 → $ 5x = 44 $

10. *A number plus that number squared is equal to fifty-six.*
→ “a number” = $ x $
→ “that number squared” = $ x^2 $
→ sum = $ x + x^2 $
→ equals 56 → $ x^2 + x = 56 $ (or $ x + x^2 = 56 $ — same thing)

Let me double-check each for correctness:

1. ✔ $ x^2 = 1936 $
2. ✔ $ x - 20 = 0 $
3. ✔ $ 64x = 88 $
4. ✔ $ x^3 = 64 $
5. ✔ $ x - 12 = 36 $
6. ✔ $ x + 8 = 22 $
7. ✔ $ -12x = 26 $
8. ✔ $ x - 12 = 22 $
9. ✔ $ 5x = 44 $
10. ✔ $ x^2 + x = 56 $

All look correct.

Final Answer:
1) $ x^2 = 1936 $
2) $ x - 20 = 0 $
3) $ 64x = 88 $
4) $ x^3 = 64 $
5) $ x - 12 = 36 $
6) $ x + 8 = 22 $
7) $ -12x = 26 $
8) $ x - 12 = 22 $
9) $ 5x = 44 $
10) $ x^2 + x = 56 $