Step 1: Write the Inequality

The problem states Chelsea starts with $200 and withdraws $15 every week, maintaining a balance of at least $65. Let $x$ represent the number of weeks she makes withdrawals.

The inequality is:
$200 - 15x \geq 65$

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Step 2: Solve the Equation to Find the Boundary

We need to solve the equation $200 - 15x = 65$ to determine the maximum number of weeks she can make withdrawals.

1. Subtract 65 from 200: $200 - 65 = 135$
2. Divide by 15: $x = \frac{135}{15} = 9$

So, the boundary value is $x = 9$. This means Chelsea can withdraw money for exactly 9 weeks before the balance drops below $65.

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Step 3: Fill in the Truth Table for Different Values of $x$

Now let’s plug in values below, at, and above the boundary to see if the inequality $200 - 15x \geq 65$ holds.

x	Expression	Result	Inequality True/False
8	$200 - 15(8) = 80$	$80 \geq 65$	True
9	$200 - 15(9) = 65$	$65 \geq 65$	True
10	$200 - 15(10) = 50$	$50 \geq 65$	False

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Step 4: Write the Solution to the Inequality

From the truth table, we see that:

• The inequality is True when $x = 8$ and $x = 9$.
• The inequality becomes False when $x = 10$.

Thus, the solution to the inequality is: $x \leq 9$

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Step 5: Interpret the Meaning of $x \leq 9$

What does $x \leq 9$ mean in this problem?

• Correct Answer: Chelsea has been withdrawing money for exactly 9 weeks or less than 9 weeks.

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Let me know if you have any further questions!
Here are five related questions to deepen your understanding:

1. What would the inequality look like if Chelsea started with $300 instead?
2. How would the solution change if the minimum balance needed was $100?
3. If Chelsea deposits $10 each week instead of withdrawing, what would the new inequality be?
4. How many weeks would it take for Chelsea's account to be empty if she continues withdrawing $15 each week?
5. What if the amount she withdraws each week increases to $20? How would that change the inequality?

Tip: When solving inequalities, always remember to carefully handle signs when dividing or multiplying by negative numbers!