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

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-\infty, 3]

\newline

Choices:

\newline

(A)

x < 3

\newline

(B)

x \geq 3

\newline

(C)

x \leq 3

\newline

(D)

x > 3

Identify Endpoints: Identify the endpoints of the interval and whether they are included in the set. The interval is $(-\infty, 3]$ , which means that the endpoint $3$ is included, but $-\infty$ is never included because it is not a finite number.
Determine Inequality: Determine the inequality that corresponds to the interval. Since $3$ is included, we use the ＂less than or equal to＂ symbol ( $\leq$ ) for the endpoint $3$ . The interval extends to negative infinity, which means all numbers less than or equal to $3$ are included.
Match with Choices: Match the correct inequality with the given choices. The interval $(-\infty, 3]$ corresponds to the inequality $x \leq 3$ , which is choice (C).

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