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What inequality represents this interval? $\newline$ $(-3, 5]$ $\newline$ Choices: $\newline$ (A) $-3 \leq x < 5$ $\newline$ (B) $-3 \leq x \leq 5$ $\newline$ (C) $-3 < x < 5$ $\newline$ (D) $-3 < x \leq 5$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-3, 5]

\newline

Choices:

\newline

(A)

-3 \leq x < 5

\newline

(B)

-3 \leq x \leq 5

\newline

(C)

-3 < x < 5

\newline

(D)

-3 < x \leq 5

Identify Endpoints: Identify the endpoints of the interval and whether they are included in the interval. The interval is $(-3, 5]$ , which means $-3$ is not included (denoted by the parenthesis), and $5$ is included (denoted by the bracket).
Translate to Inequality: Translate the interval into an inequality. Since $-3$ is not included, the inequality must use a less than symbol for the lower bound. Since $5$ is included, the inequality must use a less than or equal to symbol for the upper bound.
Write Correct Inequality: Write the inequality using the correct symbols. The inequality that represents the interval $-3, 5]$ is $-3 < x \leq 5$ .

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