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What inequality represents this interval? $\newline$ $(-\infty, -4)$ $\newline$ Choices: $\newline$ (A) $x \geq -4$ $\newline$ (B) $x > -4$ $\newline$ (C) $x < -4$ $\newline$ (D) $x \leq -4$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-\infty, -4)

\newline

Choices:

\newline

(A)

x \geq -4

\newline

(B)

x > -4

\newline

(C)

x < -4

\newline

(D)

x \leq -4

Identify Characteristics: Identify the characteristics of the interval $(-\infty, -4)$ . The interval starts from negative infinity and goes up to, but does not include, $-4$ .
Determine Inclusion: Determine if the endpoint $-4$ is included in the interval. Since the interval is $(-\infty, -4)$ , the parenthesis indicates that $-4$ is not included.
Translate into Inequality: Translate the interval into an inequality. Since the interval goes up to but does not include $-4$ , the inequality must be ＂less than＂ and not ＂less than or equal to＂. Therefore, the correct inequality is $x < -4$ .

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\newline

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