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What inequality represents this interval? $\newline$ $(3, 7]$ $\newline$ Choices: $\newline$ (A) $3 < x \leq 7$ $\newline$ (B) $3 < x < 7$ $\newline$ (C) $3 \leq x \leq 7$ $\newline$ (D) $\(3\) \leq x < \(7\)

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(3, 7]

\newline

Choices:

\newline

(A)

3 < x \leq 7

\newline

(B)

3 < x < 7

\newline

(C)

3 \leq x \leq 7

\newline

(D) $\(3\) \leq x < \(7\)

Identify Characteristics: Identify the characteristics of the interval $(3, 7]$ . The parenthesis ' $' indicates that \$3$ is not included in the interval, while the bracket '\]' indicates that $7$ is included in the interval.
Translate to Inequality: Translate the interval notation into an inequality. Since $3$ is not included, we use a strict inequality for $3$ . Since $7$ is included, we use a non-strict inequality for $7$ .
Write Matching Inequality: Write the inequality that matches the interval. The inequality that represents the interval $(3, 7]$ is $3 < x \leq 7$ .

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\newline

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