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What interval does this inequality represent? $\newline$ $3 < x \leq 6$ $\newline$ Choices: $\newline$ (A) $[3, 6]$ $\newline$ (B) $[3, 6)$ $\newline$ (C) $(3, 6)$ $\newline$ (D) $(3, 6]$

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Interval notation

Full solution

Q. What interval does this inequality represent?

\newline

3 < x \leq 6

\newline

Choices:

\newline

(A)

[3, 6]

\newline

(B)

[3, 6)

\newline

(C)

(3, 6)

\newline

(D)

(3, 6]

Identify Endpoints: Identify the endpoints of the interval for the inequality $3 < x \leq 6$ . The endpoints are $3$ and $6$ .
Check Inclusion: Check whether the endpoints are included or not. In the inequality $3 < x \leq 6$ , $3$ is not included because the inequality is strict ( $3 < x$ ), but $6$ is included because the inequality is non-strict ( $x \leq 6$ ).
Determine Interval: Determine the interval that the inequality $3 < x \leq 6$ represents. Since $3$ is not included, we use a parenthesis. Since $6$ is included, we use a bracket. The interval is therefore $(3, 6]$ .

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