Algebra Writing Verbal Statements as Algebraic Equations Math - Free Printable

Let's go through each problem on the worksheet and write the correct algebraic expression or equation, then explain how to solve it.

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1.) A number minus 18

- Expression: $ n - 18 $
- ✔ Correct.
- *Explanation:* "A number" is represented by $ n $, and "minus 18" means subtract 18 from it.

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2.) A number decreased by 16

- Expression: $ n - 16 $
- ✔ Correct.
- *Explanation:* "Decreased by" means subtraction. So, $ n - 16 $.

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3.) x plus twelve is twenty one

- Equation: $ x + 12 = 21 $
- ✔ Correct.
- *Explanation:* "Plus" means addition, "is" means equals. So: $ x + 12 = 21 $

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4.) x times twelve is forty-six

- Equation: $ x \cdot 12 = 46 $
- ✔ Correct (though sometimes written as $ 12x = 46 $).
- *Explanation:* "Times" means multiplication. So $ 12x = 46 $

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5.) six increased by twelve

- Expression: $ 6 + 12 $
- ✔ Correct.
- *Explanation:* "Increased by" means add. So $ 6 + 12 = 18 $. This is a numerical expression.

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6.) two times eight

- Expression: $ 2 \cdot 8 $
- ✔ Correct.
- *Explanation:* Multiplication: $ 2 \times 8 = 16 $

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7.) six more than twice a number

- Expression: $ 2n + 6 $
- ✔ Correct.
- *Explanation:* "Twice a number" = $ 2n $, "six more than" means add 6 → $ 2n + 6 $

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8.) eight divided by twice a number

- Expression: $ \frac{8}{2n} $ or $ \frac{8}{2n} $
- ✔ The answer given is $ 2n + 8 $ or $ \frac{8}{2n} $ — this is incorrect.
- $ 2n + 8 $ means "twice a number plus eight", which is not the same.
- But $ \frac{8}{2n} $ is correct.
- ✘ Correction: Only $ \frac{8}{2n} $ is correct.
- *Explanation:* "Twice a number" = $ 2n $, "eight divided by" that → $ \frac{8}{2n} $

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9.) The sum of seven and x

- Expression: $ 7 + x $
- ✔ Correct.
- *Explanation:* "Sum" means addition. So $ 7 + x $

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10.) x times eleven is equal to thirty-three

- Equation: $ x \cdot 11 = 33 $
- ✔ Correct.
- *Explanation:* "Times" = multiplication, "is equal to" = $ = $ → $ 11x = 33 $

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11.) The difference between x and eight is equal to fifteen

- Equation: $ x - 8 = 15 $
- ✔ Correct.
- *Explanation:* "Difference" means subtraction. Since it says "between x and eight", we assume $ x - 8 $ (unless specified otherwise). So $ x - 8 = 15 $

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✔ Summary of Corrections:

Only #8 has an error in the provided answer.

#### Corrected #8:
> 8.) eight divided by twice a number
> Answer: $ \frac{8}{2n} $
> *(Not $ 2n + 8 $)*

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Final Answers:

| # | Problem | Correct Algebraic Expression |
|----|--------|-------------------------------|
| 1 | A number minus 18 | $ n - 18 $ |
| 2 | A number decreased by 16 | $ n - 16 $ |
| 3 | x plus twelve is twenty one | $ x + 12 = 21 $ |
| 4 | x times twelve is forty-six | $ 12x = 46 $ |
| 5 | six increased by twelve | $ 6 + 12 $ |
| 6 | two times eight | $ 2 \cdot 8 $ |
| 7 | six more than twice a number | $ 2n + 6 $ |
| 8 | eight divided by twice a number | $ \frac{8}{2n} $ |
| 9 | The sum of seven and x | $ 7 + x $ |
| 10 | x times eleven is equal to thirty-three | $ 11x = 33 $ |
| 11 | The difference between x and eight is equal to fifteen | $ x - 8 = 15 $ |

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✔ All others are correct! Just fix #8.

Let me know if you want solutions to the equations (like solving for $ x $) as well!