To determine how many weeks Jacob can withdraw $40 while keeping his balance above $400, we start by calculating his account balance after \( x \) weeks.
Jacob starts with $1,000 and withdraws $40 each week. Therefore, after \( x \) weeks, his balance will be:
\[ 1000 - 40x \]
We need to ensure that this balance remains greater than $400 since the account requires a minimum balance of more than $400. This can be expressed as the inequality:
\[ 1000 - 40x > 400 \]
Now, we can solve this inequality:
- Subtract 1000 from both sides:
\[ -40x > 400 - 1000 \] \[ -40x > -600 \]
- Divide both sides by -40. Remember, when dividing or multiplying by a negative number, the inequality sign flips.
\[ x < \frac{-600}{-40} \] \[ x < 15 \]
Therefore, the inequality that models the number of weeks \( x \) that Jacob can withdraw $40, while maintaining the minimum balance requirement, is:
\[ x < 15 \]
The correct answer is:
D. x < 15