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What inequality represents this interval? $\newline$ $(-8, -1]$ $\newline$ Choices: $\newline$ (A) $-8 \leq x < -1$ $\newline$ (B) $-8 < x \leq -1$ $\newline$ (C) $-8 < x < -1$ $\newline$ (D) $-8 \leq x \leq -1$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-8, -1]

\newline

Choices:

\newline

(A)

-8 \leq x < -1

\newline

(B)

-8 < x \leq -1

\newline

(C)

-8 < x < -1

\newline

(D)

-8 \leq x \leq -1

Identify Characteristics: Identify the characteristics of the interval $(-8, -1]$ . The interval starts at $-8$ and ends at $-1$ . The parenthesis around $-8$ indicates that $-8$ is not included in the interval, while the square bracket around $-1$ indicates that $-1$ is included in the interval.
Translate into Inequality: Translate the interval into an inequality. Since $-8$ is not included, we use a less than symbol for the lower bound. Since $-1$ is included, we use a less than or equal to symbol for the upper bound. This gives us the inequality $-8 < x \leq -1$ .
Match to Choices: Match the inequality to the given choices. The inequality we found in Step $2$ is $-8 < x \leq -1$ , which corresponds to choice $(B)$ .

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