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What inequality represents this interval? $\newline$ $(-9, -5)$ $\newline$ Choices: $\newline$ (A) $-9 < x < -5$ $\newline$ (B) $-9 < x \leq -5$ $\newline$ (C) $-9 \leq x < -5$ $\newline$ (D) $-9 \leq x \leq -5$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-9, -5)

\newline

Choices:

\newline

(A)

-9 < x < -5

\newline

(B)

-9 < x \leq -5

\newline

(C)

-9 \leq x < -5

\newline

(D)

-9 \leq x \leq -5

Identify Endpoints: Identify the endpoints of the interval and whether they are included in the interval. The interval is $(-9, -5)$ , which means that $-9$ is not included and $-5$ is not included.
Translate to Inequality: Translate the interval into an inequality. Since $-9$ is not included, the inequality must be strict on the left side, using ＂ $<$ ＂. Similarly, since $-5$ is not included, the inequality must also be strict on the right side, using ＂ $<$ ＂.
Write Inequality: Write the inequality using the information from the previous steps. The inequality that represents the interval $(-9, -5)$ is $-9 < x < -5$ .
Match with Choices: Match the inequality with the given choices. The correct inequality is $(A) -9 < x < -5$ .

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