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What interval does this inequality represent? $\newline$ $-7 < x \leq -1$ $\newline$ Choices: $\newline$ (A) $(-7, -1]$ $\newline$ (B) $[-7, -1]$ $\newline$ (C) $(-7, -1)$ $\newline$ (D) $[-7, -1)$

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Interval notation

Full solution

Q. What interval does this inequality represent?

\newline

-7 < x \leq -1

\newline

Choices:

\newline

(A)

(-7, -1]

\newline

(B)

[-7, -1]

\newline

(C)

(-7, -1)

\newline

(D)

[-7, -1)

Identify Endpoints: Identify the endpoints of the interval for the inequality $-7 < x \leq -1$ . The endpoints are $-7$ and $-1$ .
Check Inclusion: Check whether the endpoints are included or not. In the inequality $-7 < x \leq -1$ , $-7$ is not included because the inequality is strict (indicated by ＂<＂), but $-1$ is included because the inequality is non-strict (indicated by ＂\leq＂).
Determine Interval Type: Determine the interval that the inequality $-7 < x \leq -1$ represents. Since $-7$ is not included, we use a parenthesis $($ . Since $-1$ is included, we use a bracket $]$ .
Write Interval Notation: Write the interval notation based on the previous steps. The correct interval notation is $(-7, -1]$ .

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