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Answer :
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].
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].
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Rewritten by : Barada
