Michael starts with $250 in his bank account. Every week he withdraws $20 for miscellaneous expenses. For how many weeks could he withdraw the money if he maintains a balance of at least $90?
Write an inequality to represent the situation. Use x to represent the number of weeks.
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 250 - 20x = 90, to find the boundary for the inequality. Show your work or solve on paper.
250 - 20x ≥ 90
250−20x
=
90
 
x
=
You got it!
Fill in the table to show whether a value below the boundary, the boundary, and a value above the boundary make the inequality true or false.
x= 7	x=8 (boundary)	x= 9
250 - 20x ≥ 90	


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.

---

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!

Michael starts with $250 in his bank account. Every week he withdraws $20 for miscellaneous expenses. For how many weeks could he withdraw the money if he maintains a balance of at least $90? Write an inequality to represent the situation. Use x to represent the number of weeks.

Learn how to solve a linear inequality representing Michael's weekly withdrawals from his $250 bank account. This step-by-step guide shows how to maintain a balance of at least $90 while withdrawing $20 weekly. Suitable for students in Grades 6-8.

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