https://file.aiquickdraw.com/mathbot/file/1728619915792180t9sha.pdf

Here are the answers to the questions from the uploaded file:

1. **Graph the inequality $ x \geq 2 $**:
   - On the number line, mark a closed circle at 2 and shade to the right to show all values greater than or equal to 2.

2. **Graph the inequality $ -3 < x \leq 1 $**:
   - On the number line, mark an open circle at -3 (since $x$ cannot be equal to -3) and a closed circle at 1 (since $x$ can be equal to 1). Shade the region between -3 and 1.

3. **Graph the inequality $ |x - 1| \geq 3 $**:
   - This inequality can be rewritten as $ x - 1 \geq 3 $ or $ x - 1 \leq -3 $, which simplifies to $ x \geq 4 $ or $ x \leq -2 $.
   - On the number line, mark closed circles at -2 and 4, and shade the regions to the left of -2 and the right of 4.

4. **Cost of a taxi ride for 2.75 miles**:
   - The total cost is calculated using the formula $ 5 + 0.25 \times \left(\frac{2.75}{0.125}\right) $.
   - This simplifies to $ 5 + 0.25 \times 22 = 5 + 5.50 = 10.50 $.
   - The total cost is **$10.50**.

5. **Cost for Justin to go to the fair**:
   - The total cost is calculated using the formula $ 4.50 + 0.10 \times 56 $.
   - This simplifies to $ 4.50 + 5.60 = 10.10 $.
   - Justin will need **$10.10**.

6. **Kelvin's coffee blend**:
   - Let $ x $ represent the pounds of the $3.20 coffee, and $ 9.6 - x $ represent the pounds of the $4.60 coffee.
   - The equation for the total cost is $ 3.20x + 4.60(9.6 - x) = 38 $.
   - Simplifying this: $ 3.20x + 44.16 - 4.60x = 38 $, which simplifies to $ -1.4x = -6.16 $, so $ x = 4.4 $.
   - Kelvin should use **4.4 pounds of $3.20 coffee** and **5.2 pounds of $4.60 coffee**.

7. **Number of nickels in the bank**:
   - Let $ x $ represent the number of nickels, and $ 22 - x $

Solve real-life word problems like calculating taxi fare for a 2.75-mile ride, determining the total cost for Justin at the county fair, and mixing coffee blends. Also, learn to graph inequalities such as x ≥ 2 and |x−1| ≥ 3. This resource is perfect for students in Grades 9-12, covering essential algebraic concepts and linear equations.

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