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Thaavik · Answer 1 · 2023-07-07T09:07:00+0000

A number x is in a given interval (a,b) if it satisfies the following inequalities:

$\begin{gathered} x>a, \\ xNotice that:<p>1)</p>[tex]\begin{gathered} -(9)/(2)>-\infty, \\ -(9)/(2)=3\cdot(-(3)/(2))<-(3)/(2)\text{.} \end{gathered}$

Therefore -9/2 is in the given interval.

2)

$\begin{gathered} -1>-\infty, \\ -1=-(2)/(2)>-(2)/(2)-(1)/(2)=-(3)/(2)\text{.} \end{gathered}$

Therefore -1 is not in the given interval.

3)

$\begin{gathered} -(3)/(2)>-\infty, \\ -(3)/(2)=-(3)/(2)\text{.} \end{gathered}$

Therefore -3/2 is not in the given interval.

4)

$\begin{gathered} (1)/(2)>-\infty, \\ (1)/(2)>0>-(3)/(2)\text{.} \end{gathered}$

Therefore 1/2 is not in the given interval.

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