broall wrote:

Bunuel wrote:

Which of the following expresses the range of possible values for t if 0 < |5t − 8| < 1?

A. 2/5 < t < 14/5

B. 2/5 < t < 9/5

C. 7/5 < t < 14/5

D. 7/5 < t < 9/5

E. 9/5 < t < 14/5

Solve for the inequality \(0 < |5t − 8| < 1\)

\(|5t − 8| > 0 \implies t \neq \frac{8}{5}\)

\(|5t − 8| < 1 \implies -1 < 5t-8 < 1 \implies 7 < 5t < 9 \implies \frac{7}{5} < t < \frac{9}{5}\)

It seems that there is no answer satisfied the inequality.

The answer will be D if the condition \(0 < |5t − 8|\) doesn't exist in the inequality.

Broall, how do you know to drop the modulus and make the outliers -1 and 1? For me, I originally came up with \(\frac{8}{5}\)<t<\(\frac{9}{5}\). I just added 8 to both sides and then divided by 5. What is wrong with this solution and how should I approach questions like this in the future?

Thanks,

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