To translate the sentence "The difference of –3.2 and the sum of a number and 19.1 is at most 14.2" into an inequality, we need to break it down:
- The phrase "the sum of a number and 19.1" can be represented as \(x + 19.1\).
- The phrase "the difference of –3.2 and..." means we subtract the sum from -3.2, which can be represented as \(-3.2 - (x + 19.1)\).
- The phrase "is at most 14.2" translates to "less than or equal to 14.2", which means we will use the \(\leq\) sign.
Putting it all together, we have:
\[ -3.2 - (x + 19.1) \leq 14.2 \]
This corresponds to the first option:
Negative 3.2 minus (x + 19.1) less-than-or-equal-to 14.2.