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Which is the set of numbers less than $-7$ or greater than or equal to $-4$ ? $\newline$ Choices: $\newline$ (A) $\{x | x < -7 \text{ and } x \geq -4\}$ $\newline$ (B) $\{x | x < -7 \text{ or } x > -4\}$ $\newline$ (C) $\{x | x < -7 \text{ or } x \geq -4\}$ $\newline$ (D) $\{x | x > -7 \text{ or } x \leq -4\}$

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Set-builder notation

Full solution

Q. Which is the set of numbers less than

-7

or greater than or equal to

-4

?

\newline

Choices:

\newline

(A)

\{x | x < -7 \text{ and } x \geq -4\}

\newline

(B)

\{x | x < -7 \text{ or } x > -4\}

\newline

(C)

\{x | x < -7 \text{ or } x \geq -4\}

\newline

(D)

\{x | x > -7 \text{ or } x \leq -4\}

Understand the problem: Understand the problem. We need to find the set of numbers that are either less than $-7$ or greater than or equal to $-4$ . This is a union of two conditions.
Identify inequality signs: Identify the correct inequality signs for each condition. For numbers less than $-7$ , we use the $＂<＂$ sign. For numbers greater than or equal to $-4$ , we use the $＂≥＂$ sign.
Translate into set notation: Translate the conditions into set notation. The first condition is $x < -7$ . The second condition is $x \geq -4$ . Since the problem asks for numbers that satisfy either condition, we use the word $\text{or}$ to combine them.
Eliminate incorrect choices: Look at the choices and eliminate the incorrect ones. Choice (A) uses ＂and＂ which is not correct because we are looking for a union, not an intersection. Choice (B) has the wrong inequality for the second condition; it should be ＂ $x \geq -4$ ＂, not ＂ $x > -4$ ＂. Choice (D) has the wrong inequality for the first condition; it should be ＂ $x < -7$ ＂, not ＂ $x > -7$ ＂.
Select correct choice: Select the correct choice. The only choice that correctly represents the union of the two conditions is (C) ${x | x < -7 \text{ or } x \geq -4}$ .

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