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What interval does this inequality represent? $\newline$ $-5 < x \leq -1$ $\newline$ Choices: $\newline$ (A) $(-5, -1]$ $\newline$ (B) $[-5, -1]$ $\newline$ (C) $[-5, -1)$ $\newline$ (D) $(-5, -1)$

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Interval notation

Full solution

Q. What interval does this inequality represent?

\newline

-5 < x \leq -1

\newline

Choices:

\newline

(A)

(-5, -1]

\newline

(B)

[-5, -1]

\newline

(C)

[-5, -1)

\newline

(D)

(-5, -1)

Identify Endpoints: Identify the endpoints of the interval for the inequality $-5 < x \leq -1$ . The endpoints are $-5$ and $-1$ .
Check Inclusion: Check whether each endpoint is included in the interval. For $-5 < x$ , $-5$ is not included because the inequality is strict (less than, not less than or equal to). For $x \leq -1$ , $-1$ is included because the inequality is non-strict (less than or equal to).
Determine Interval: Determine the interval that the inequality $-5 < x \leq -1$ represents. Since $-5$ is not included, we use a parenthesis. Since $-1$ is included, we use a bracket. Therefore, the interval is $(-5, -1]$ .

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