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Solve the inequality.

A journalist is assigned to write a story that is 1,200 words long. To fit in the publication's available space, the story's length can vary by no more than 75 words.

Which word counts would be accepted by the journalist's publication?

\begin{tabular}{|c|c|c|c|c|}
\hline \multicolumn{5}{|c|}{ Word Counts } \\
\hline 1,100 & 1,125 & 1,260 & 1,290 & 1,300 \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine which word counts would be accepted by the journalist's publication, we will follow these steps:

1. Identify the initial word count and the allowed variation:
- Initial word count: 1,200 words
- Allowed variation: 75 words

2. Calculate the acceptable range:
- Lower limit: 1,200 - 75 = 1,125 words
- Upper limit: 1,200 + 75 = 1,275 words

3. Evaluate each word count against the acceptable range:
- Word count 1,100: This is less than the lower limit of 1,125, so it is not accepted.
- Word count 1,125: This is exactly the lower limit, so it is accepted.
- Word count 1,260: This is within the range (between 1,125 and 1,275), so it is accepted.
- Word count 1,290: This is greater than the upper limit of 1,275, so it is not accepted.
- Word count 1,300: This is also greater than the upper limit, so it is not accepted.

Accepted word counts:
- 1,125
- 1,260

So, among the given word counts, the values that would be accepted by the journalist's publication are 1,125 and 1,260.

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