Writing Inequalities from Word Problems - Free Printable

Thank you for uploading the image. Since I cannot view images directly, I’ll rely on your description or any text you’ve provided. However, based on your message and the filename “INEQUALITIES FROM WORD PROBLEMS A1,” I can infer that this is a worksheet containing word problems that require setting up and solving inequalities.

Since you mentioned “solve the problem and explain the solution,” but didn’t specify which of the 10 problems you’d like solved, I’ll pick Problem #1 as an example — it’s typically the first and most straightforward — and solve it step by step. If you want another problem solved, just let me know!

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📝 Problem #1 (Inferred from typical worksheets):

> A company wants to rent a bus for a field trip. The bus rental costs $250 plus $0.50 per mile driven. The company has a budget of no more than $300. Write and solve an inequality to find how many miles they can drive.

*(Note: This is a reconstructed version based on common textbook problems. If your actual Problem #1 differs, please paste the text.)*

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## ✔ Step-by-Step Solution:

Step 1: Define the variable

Let m = number of miles driven.

Step 2: Write the cost expression

The total cost = fixed cost + variable cost
→ Total cost = 250 + 0.50m

Step 3: Set up the inequality

The company can spend no more than $300, so:
> 250 + 0.50m ≤ 300

Step 4: Solve the inequality

Subtract 250 from both sides:
> 0.50m ≤ 50

Divide both sides by 0.50:
> m ≤ 100

✔ Final Answer:

The company can drive at most 100 miles.

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## 🧠 Explanation:

This problem models a real-world budget constraint. The inequality ensures that the total cost (fixed + per-mile) does not exceed the available budget. Solving it gives the maximum allowable miles within that budget.

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## 💡 Tip for Word Problems:
Always:
1. Identify what you’re solving for → assign a variable.
2. Translate words into math → find relationships.
3. Set up the inequality using keywords like “at most,” “no more than,” “at least,” etc.
4. Solve algebraically.
5. Interpret the answer in context.

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If you’d like me to solve another specific problem from your worksheet (e.g., #3, #7, etc.), please copy and paste the exact text of that problem here — I’ll solve it with full explanation!

Also, if you can describe the image content (e.g., “Problem 5 says...”), I can tailor the solution precisely.

Let me know how else I can help! 😊