To solve this problem, we need to find the inequality that represents the time [tex]\(x\)[/tex] in minutes for Amy to finish typing the remaining words of her paper.
Let's break this down step-by-step:
1. Identify Variables and Given Information:
- Amy's typing speed: 38 words per minute
- Words Amy has already typed: 1450 words
- Total words required to finish the paper: 4000 words
2. Set Up the Equation:
We need to find out how many more words Amy has left to type. To do this, we subtract the number of words she has already typed from the total number of words:
[tex]\( \text{Words left to type} = \text{Total words} - \text{Words already typed} \)[/tex]
[tex]\[
\text{Words left to type} = 4000 - 1450 = 2550 \text{ words}
\][/tex]
3. Formulate the Rate-Time-Distance Relationship:
Amy types at a rate of 38 words per minute. We need to find the time [tex]\(x\)[/tex] in minutes needed to type the remaining 2550 words. Using the rate [tex]\( \text{rate} \times \text{time} = \text{distance} \)[/tex], we have:
[tex]\[
38 \times x = 2550 \text{ words}
\][/tex]
4. Convert this into an Inequality:
To express this as an inequality, since we are interested in the time [tex]\(x\)[/tex] needed to ensure she has typed more than 4000 words in total, we reframe it:
[tex]\[
38x + 1450 > 4000
\][/tex]
So the correct inequality that can be used to solve for [tex]\(x\)[/tex], the number of minutes needed for Amy to finish typing her paper, is:
[tex]\[
38x + 1450 > 4000
\][/tex]
Therefore, the correct option is D.
