Let's go through the steps to determine the correct expression for the employee's take-home pay.
1. Define the variables:
- Let [tex]\( x \)[/tex] be the employee's pay before any deductions.
2. Subtract tax-exempt expenses:
- According to the problem, the employee has [tex]$\$[/tex]350[tex]$ of tax-exempt expenses that are taken out first. Thus, after the tax-exempt expenses are subtracted, the remaining amount is \( x - 350 \).
3. Calculate the tax:
- The employee's taxable income is then \( x - 350 \).
- The tax rate is 15%, which means that the tax amount is \( 0.15 \times (x - 350) \).
4. Subtract the tax from the taxable income:
- After calculating the tax, we subtract this tax from the taxable income to find the take-home pay.
- The take-home pay is given by \( (x - 350) - 0.15 \times (x - 350) \).
Now, let's simplify this expression:
\[
(x - 350) - 0.15(x - 350)
\]
Factor out \( x - 350 \) from both terms:
\[
(x - 350)(1 - 0.15)
\]
Simplify the multiplication:
\[
(x - 350) \times 0.85
\]
This simplified expression represents the employee's take-home pay after the $[/tex]\[tex]$350$[/tex] of tax-exempt expenses and the 15% tax deduction.
Thus, the correct expression for the employee's take-home pay is:
[tex]\[
0.85(x - 350)
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{0.85(x-350)}
\][/tex]
