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What inequality represents this interval? $\newline$ $(2, 6)$ $\newline$ Choices: $\newline$ (A) $2 < x < 6$ $\newline$ (B) $2 \leq x < 6$ $\newline$ (C) $2 < x \leq 6$ $\newline$ (D) $2 \leq x \leq 6$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(2, 6)

\newline

Choices:

\newline

(A)

2 < x < 6

\newline

(B)

2 \leq x < 6

\newline

(C)

2 < x \leq 6

\newline

(D)

2 \leq x \leq 6

Identify Interval Type: Identify the type of interval given. The interval $(2, 6)$ is an open interval because it uses parentheses, which means that the endpoints $2$ and $6$ are not included in the interval.
Translate to Inequality: Translate the open interval into an inequality. Since $2$ is not included, the inequality must be strict on the lower bound, using ＂ $<$ ＂ rather than ＂\(\newline\)leq\(＂. Similarly, since \)\(6\) is not included, the inequality must be strict on the upper bound as well.
Write Corresponding Inequality: Write the inequality that corresponds to the open interval $(2, 6)$ . The correct inequality is $2 < x < 6$ , which means $x$ is greater than $2$ and less than $6$ .

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