https://file.aiquickdraw.com/mathbot/file/1727401377852vufmkcho.jpg

Let's analyze the problem step by step:

### Problem Breakdown:
- **Plan 1**: Charges a fixed rate of $26 per month for unlimited calls.
- **Plan 2**: Charges $14 per month, plus an additional $0.06 per call.

### Part (a):
We need to find when **Plan 1** is more economical than **Plan 2**. Let $ x $ represent the number of monthly calls.

- **Cost of Plan 1**: $26 (no matter how many calls are made)
- **Cost of Plan 2**: $14 + $0.06 per call, or $ 14 + 0.06x $

We need to find when the cost of Plan 1 is **less than** the cost of Plan 2:
\[
26 < 14 + 0.06x
\]

### Solving the inequality:
1. Subtract 14 from both sides:
   \[
   26 - 14 < 0.06x
   \]
   \[
   12 < 0.06x
   \]
2. Divide both sides by 0.06:
   \[
   \frac{12}{0.06} < x
   \]
   \[
   200 < x
   \]

So, the inequality is $ x > 200 $. This means that **Plan 1** becomes more economical when the number of monthly calls exceeds 200.

### Part (b):
The meaning of the answer $ x > 200 $ is that **if you make more than 200 calls in a month**, Plan 1 (with unlimited calls) will cost less than Plan 2 (which charges per call). If you make fewer than 200 calls, Plan 2 is the better option.

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Do you have any further questions, or would you like more details on the solution process?

Here are five related questions to further explore the concept:
1. How would the inequality change if Plan 1 charged $30 per month instead of $26?
2. What would the inequality be if Plan 2 charged $0.10 per call instead of $0.06?
3. Can you solve for the breakeven point if Plan 1 was reduced to $20 per month?
4. How would the inequality change if Plan 2 included a $5 discount after 150 calls?
5. What happens to the solution if both plans include an extra tax of $2 per month?

**Tip**: Whenever comparing costs between plans, set up the cost functions for both and solve the inequality to find the breakeven point.

The telephone company offers two billing plans for local calls. Plan 1 charges $26 per month for unlimited calls and Plan 2 charges $14 per month plus $0.06 per call. a) Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2. b) Explain the meaning of the answer to part a.

Learn how to compare two phone billing plans using algebraic inequalities. The problem involves Plan 1, which costs $26 monthly for unlimited calls, and Plan 2, which costs $14 per month plus $0.06 per call. This exercise is perfect for students in Grades 7-9 looking to strengthen their skills in linear inequalities.

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