Which is the set of integers greater than or equal to $2$ and less than $6$ ? $\newline$ Choices: $\newline$ (A) $\{3, 4, 5, 6\}$ $\newline$ (B) $\{3, 4, 5\}$ $\newline$ (C) $\{2, 3, 4, 5\}$ $\newline$ (D) $\{2, 6\}$

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Algebra 1

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Q. Which is the set of integers greater than or equal to

2

and less than

6

\newline

Choices:

\newline

(A)

\{3, 4, 5, 6\}

\newline

(B)

\{3, 4, 5\}

\newline

(C)

\{2, 3, 4, 5\}

\newline

(D)

\{2, 6\}

Identify Inequalities: Identify the inequality that represents the set of integers greater than or equal to $2$ and less than $6$ . $\newline$ We are looking for two inequalities here: one that represents ＂greater than or equal to $2$ ＂ and another that represents ＂less than $6$ ＂. $\newline$ The inequality for ＂greater than or equal to $2$ ＂ is $x \geq 2$ . $\newline$ The inequality for ＂less than $6$ ＂ is $x < 6$ .
Combine Inequalities: Combine the inequalities to form a compound inequality that represents the set of integers that satisfy both conditions. $\newline$ The compound inequality is $2 \leq x < 6$ . $\newline$ This means we are looking for integers that are both greater than or equal to $2$ and less than $6$ .
List Satisfying Integers: List the integers that satisfy the compound inequality $2 \leq x < 6$ . $\newline$ Starting from $2$ and going up to but not including $6$ , we have the integers $2$ , $3$ , $4$ , and $5$ . $\newline$ These are the integers that are greater than or equal to $2$ and less than $6$ .
Match to Choices: Match the list of integers from Step $3$ to the given choices. $\newline$ The list of integers we found is ${2, 3, 4, 5}$ . $\newline$ Looking at the choices: $\newline$ (A) ${3, 4, 5, 6}$ - This set includes $6$ , which should not be included. $\newline$ (B) ${3, 4, 5}$ - This set does not include $2$ , which should be included. $\newline$ (C) ${2, 3, 4, 5}$ - This set matches our list exactly. $\newline$ (D) ${2, 6}$ - This set does not include $3, 4,$ or $5$ , and it incorrectly includes $6$ .