Translating Linear Inequalities worksheet with problems and number line representations.

It looks like you've uploaded an image of a worksheet titled "Translating Linear Inequalities", which contains two columns of problems. The task is to translate word phrases into mathematical inequalities.

Let me go through each problem and solve it step by step, explaining how to translate the verbal descriptions into algebraic inequalities.

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Left Column (Problems 1–10)

#### 1. "x is at least 5"
- "At least" means greater than or equal to.
- So:
x ≥ 5

#### 2. "a number is no more than 10"
- "No more than" means less than or equal to.
- Let the number be $ x $.
x ≤ 10

#### 3. "the sum of a number and 8 is greater than 12"
- Let the number be $ x $.
- Sum of $ x $ and 8: $ x + 8 $
- Greater than 12:
x + 8 > 12

#### 4. "twice a number is less than 6"
- Let the number be $ x $.
- Twice the number: $ 2x $
- Less than 6:
2x < 6

#### 5. "a number is at most 15"
- "At most" means less than or equal to.
x ≤ 15

#### 6. "three times a number is not less than 18"
- "Not less than" means greater than or equal to.
- Let the number be $ x $.
- Three times: $ 3x $
3x ≥ 18

#### 7. "the difference between a number and 4 is at least 10"
- Let the number be $ x $.
- Difference: $ x - 4 $
- At least 10:
x - 4 ≥ 10

#### 8. "a number is less than or equal to 9"
- Direct translation:
x ≤ 9

#### 9. "five more than a number is greater than 20"
- Let the number be $ x $.
- Five more: $ x + 5 $
- Greater than 20:
x + 5 > 20

#### 10. "a number is more than 14"
- "More than" means greater than.
x > 14

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Right Column (Problems 11–20)

#### 11. "n is at most 12"
- "At most" → ≤
n ≤ 12

#### 12. "a number is greater than 13"
- x > 13

#### 13. "a number is less than or equal to 20"
- x ≤ 20

#### 14. "the product of a number and 4 is at least 24"
- Let the number be $ x $.
- Product: $ 4x $
- At least 24:
4x ≥ 24

#### 15. "a number is less than 7"
- x < 7

#### 16. "the quotient of a number and 3 is at most 8"
- Let the number be $ x $.
- Quotient: $ \frac{x}{3} $
- At most 8:
\frac{x}{3} ≤ 8

#### 17. "a number is at least 16"
- x ≥ 16

#### 18. "the sum of twice a number and 5 is less than 15"
- Let the number be $ x $.
- Twice the number: $ 2x $
- Sum with 5: $ 2x + 5 $
- Less than 15:
2x + 5 < 15

#### 19. "a number is not greater than 10"
- "Not greater than" means less than or equal to.
x ≤ 10

#### 20. "a number is greater than or equal to 25"
- x ≥ 25

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✔ Final Answer Summary:

| Problem | Inequality |
|--------|------------|
| 1 | $ x \geq 5 $ |
| 2 | $ x \leq 10 $ |
| 3 | $ x + 8 > 12 $ |
| 4 | $ 2x < 6 $ |
| 5 | $ x \leq 15 $ |
| 6 | $ 3x \geq 18 $ |
| 7 | $ x - 4 \geq 10 $ |
| 8 | $ x \leq 9 $ |
| 9 | $ x + 5 > 20 $ |
| 10 | $ x > 14 $ |
| 11 | $ n \leq 12 $ |
| 12 | $ x > 13 $ |
| 13 | $ x \leq 20 $ |
| 14 | $ 4x \geq 24 $ |
| 15 | $ x < 7 $ |
| 16 | $ \frac{x}{3} \leq 8 $ |
| 17 | $ x \geq 16 $ |
| 18 | $ 2x + 5 < 15 $ |
| 19 | $ x \leq 10 $ |
| 20 | $ x \geq 25 $ |

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🔍 Key Phrases to Remember:

| Phrase | Symbol |
|-------|--------|
| At least | ≥ |
| At most | ≤ |
| No more than | ≤ |
| Not less than | ≥ |
| More than | > |
| Less than | < |
| Greater than or equal to | ≥ |
| Less than or equal to | ≤ |

This worksheet helps build foundational skills in translating real-world language into mathematical expressions — essential for solving inequality word problems.

Let me know if you'd like help solving these inequalities too!