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What interval does this inequality represent? $\newline$ $-4 < x \leq 1$ $\newline$ Choices: $\newline$ (A) $(-4, 1)$ $\newline$ (B) $(-4, 1]$ $\newline$ (C) $[-4, 1)$ $\newline$ (D) $[-4, 1]$

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Interval notation

Full solution

Q. What interval does this inequality represent?

\newline

-4 < x \leq 1

\newline

Choices:

\newline

(A)

(-4, 1)

\newline

(B)

(-4, 1]

\newline

(C)

[-4, 1)

\newline

(D)

[-4, 1]

Identify Endpoints: Identify the endpoints of the interval for the inequality $-4 < x \leq 1$ . The endpoints are $-4$ and $1$ .
Check Inclusion: Check whether the endpoints are included or not. In the inequality $-4 < x \leq 1$ , $-4$ is not included because the inequality is strict ( $<$ ), but $1$ is included because the inequality is non-strict ( $\leq$ ).
Determine Interval: Determine the interval that the inequality $-4 < x \leq 1$ represents. Since $-4$ is not included, we use a parenthesis (\. Since $1$ is included, we use a bracket ]. Therefore, the interval is $(-4, 1]$ .

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