Let's work through the problem step by step.

Step 1: Write the inequality

Michael starts with $250 and withdraws $20 per week. He wants to maintain a balance of at least $90. This situation can be written as:

$250 - 20x \geq 90$

Where $x$ represents the number of weeks.

Step 2: Solve the associated equation

Now, let's solve the equation $250 - 20x = 90$ to find the boundary.

$250 - 20x = 90$

1. Subtract 250 from both sides: $-20x = 90 - 250$ $-20x = -160$

2. Divide both sides by -20: $x = \frac{-160}{-20}$ $x = 8$

So, the boundary is at $x = 8$ weeks.

Step 3: Fill in the table

Now, let's evaluate the inequality $250 - 20x \geq 90$ for values below, at, and above the boundary: $x = 7$, $x = 8$, and $x = 9$.

$250 - 20x \geq 90$

• For $x = 7$: $250 - 20(7) = 250 - 140 = 110$ $110 \geq 90$ (True)

• For $x = 8$ (boundary): $250 - 20(8) = 250 - 160 = 90$ $90 \geq 90$ (True)

• For $x = 9$: $250 - 20(9) = 250 - 180 = 70$ $70 \geq 90$ (False)

Final Table:

$x$	$250 - 20x \geq 90$	True/False
$x = 7$	$250 - 140 = 110 \geq 90$	True
$x = 8$	$250 - 160 = 90 \geq 90$	True
$x = 9$	$250 - 180 = 70 \geq 90$	False

Thus, Michael can withdraw money for up to 8 weeks while maintaining a balance of at least $90.

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Would you like any more details or explanations on this?

Here are 5 related questions you can try:

1. What if Michael increased his withdrawals to $25 per week? How many weeks could he withdraw while keeping a balance of at least $90?
2. How much balance would he have after 10 weeks of withdrawing $20 per week?
3. If Michael deposited $50 every 4 weeks while withdrawing $20 weekly, how would the inequality change?
4. How would the solution change if Michael wanted to maintain a balance of at least $100 instead of $90?
5. What is the total amount Michael would have withdrawn after 6 weeks?

Tip: When solving inequalities, remember that dividing or multiplying by a negative number reverses the inequality sign!