Gray Donnelly
02/20/2024 · High School

Sea \( S=\left[\frac{-3}{4},-\frac{1}{3}\right) \cup\left(\frac{4}{3}, \frac{7}{4}\right] \)

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Step-by-step Solution

The set \( S \) is defined as the union of two intervals: 1. The first interval is \( \left[\frac{-3}{4}, -\frac{1}{3}\right) \), which includes all numbers \( x \) such that \( -\frac{3}{4} \leq x < -\frac{1}{3} \). This interval includes the left endpoint \( -\frac{3}{4} \) but does not include the right endpoint \( -\frac{1}{3} \). 2. The second interval is \( \left(\frac{4}{3}, \frac{7}{4}\right] \), which includes all numbers \( x \) such that \( \frac{4}{3} < x \leq \frac{7}{4} \). This interval does not include the left endpoint \( \frac{4}{3} \) but includes the right endpoint \( \frac{7}{4} \). To summarize, the set \( S \) can be expressed as: \[ S = \left[\frac{-3}{4}, -\frac{1}{3}\right) \cup \left(\frac{4}{3}, \frac{7}{4}\right] \] This means that \( S \) contains all numbers in the first interval and all numbers in the second interval. If you have any specific questions or need further analysis regarding this set, feel free to ask!

Quick Answer

The set \( S \) is the union of two intervals: \( \left[\frac{-3}{4}, -\frac{1}{3}\right) \) and \( \left(\frac{4}{3}, \frac{7}{4}\right] \).
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