To find the price the customer will pay for the shirt, we need to follow these steps:
1. Determine the sale price of the shirt:
The original price of the shirt is [tex]$\( x \) dollars. The shirt is on sale for 15% off. This means the sale price is 85% of the original price.
\[
\text{Sale Price} = x \times (1 - 0.15) = x \times 0.85
\]
2. Apply the coupon discount:
The customer has a coupon for $[/tex][tex]\( s \)[/tex] dollars off the sale price. We subtract the coupon discount from the sale price to get the final price the customer will pay.
[tex]\[
\text{Final Price} = \text{Sale Price} - s = (x \times 0.85) - s
\][/tex]
Therefore, the price in dollars the customer will pay for the shirt, excluding tax, is given by:
[tex]\[
\boxed{0.85x - s}
\][/tex]
