To determine the employee's take-home pay after tax deductions, let's follow the given steps.
1. Initial Variables: Let [tex]\( x \)[/tex] represent the employee's pay before any deductions.
2. Tax-Exempt Expenses: According to the problem, there are [tex]\(\$ 350\)[/tex] of tax-exempt expenses that are deducted from the total pay before calculating taxable income.
So, the taxable income is [tex]\( x - 350 \)[/tex].
3. Tax Calculation: Fifteen percent of the taxable income is collected as tax.
Therefore, the tax amount is given by [tex]\( 0.15 \times (x - 350) \)[/tex].
4. Take-Home Pay Calculation: The take-home pay is the employee's initial pay minus both the tax-exempt expenses and the taxes. This can be expressed as:
[tex]\[
\text{Take-home pay} = (\text{Initial pay} - \text{Tax amount}) - (\text{tax-exempt expenses})
\][/tex]
Plugging in the given deductions, the take-home pay formula is:
[tex]\[
\text{Take-home pay} = (x - 350) - 0.15 \times (x - 350)
\][/tex]
5. Simplify the Expression: Notice that:
[tex]\[
\text{Take-home pay} = x - 350 - 0.15 \times (x - 350)
= (x - 350)(1 - 0.15)
= (x - 350) \times 0.85
\][/tex]
Thus, the correct expression that represents the employee's take-home pay after these deductions is [tex]\( 0.85(x - 350) \)[/tex].
Considering the multiple choice options, the answer is:
[tex]\[ 0.85(x - 350) \][/tex]
Therefore, the correct option is:
[tex]\[ \mathbf{0.85(x - 350)} \][/tex]
This corresponds to the third option. Therefore, the correct answer is:
[tex]\[
\boxed{3}
\][/tex]
