Write an inequality that represents the statement "[tex]$x$[/tex] is at most -5 or at least 7."

A. [tex]$x \ \textless \ -5$[/tex] or [tex]$x \ \textgreater \ 7$[/tex]

B. [tex]$x \ \textgreater \ -5$[/tex] or [tex]$x \ \textless \ 7$[/tex]

C. [tex]$x \leq -5$[/tex] or [tex]$x \geq 7$[/tex]

D. [tex]$x \geq -5$[/tex] or [tex]$x \leq 7$[/tex]

Please select the best answer from the choices provided:

A

B

C

D

To solve the problem, we start by breaking down the statement into two parts:

1. The phrase “[tex]$ x $[/tex] is at most [tex]$-5$[/tex]” means that [tex]$ x $[/tex] can be equal to or less than [tex]$-5$[/tex]. In mathematical notation, this is written as:
[tex]$$
x \leq -5.
$$[/tex]

2. The phrase “[tex]$ x $[/tex] is at least [tex]$ 7 $[/tex]” means that [tex]$ x $[/tex] can be equal to or greater than [tex]$ 7 $[/tex]. This is written as:
[tex]$$
x \geq 7.
$$[/tex]

Since the statement uses “or,” it indicates that [tex]$ x $[/tex] can satisfy either one of these conditions. Therefore, the combined inequality is:
[tex]$$
x \leq -5 \quad \text{or} \quad x \geq 7.
$$[/tex]

Among the provided choices:

A. [tex]$ x < -5 $[/tex] or [tex]$ x > 7 $[/tex]
B. [tex]$ x > -5 $[/tex] or [tex]$ x < 7 $[/tex]
C. [tex]$ x \leq -5 $[/tex] or [tex]$ x \geq 7 $[/tex]
D. [tex]$ x \geq -5 $[/tex] or [tex]$ x \leq 7 $[/tex]

The correct representation is choice C.

Thus, the best answer is:

C. [tex]$ x \leq -5 $[/tex] or [tex]$ x \geq 7 $[/tex].