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If [tex]$x$[/tex] is a negative number, which of the following statements is false?

A. [tex]$x$[/tex] is to the left of zero.
B. [tex][tex]$-x$[/tex][/tex] is to the left of zero.
C. [tex]$x \ \textless \ 0$[/tex]
D. [tex]$-x \ \textgreater \ 0$[/tex]

Sagot :

GinnyAnswer
Let's analyze each statement one by one, given that [tex]\( x \)[/tex] is a negative number.

1. Statement: [tex]\( x \)[/tex] is to the left of zero.
- Since [tex]\( x \)[/tex] is a negative number, it is indeed to the left of zero on the number line. Therefore, this statement is true.

2. Statement: [tex]\( -x \)[/tex] is to the left of zero.
- When [tex]\( x \)[/tex] is a negative number, [tex]\( -x \)[/tex] becomes a positive number (since the negation of a negative is positive). Positive numbers are to the right of zero on the number line. Therefore, this statement is false.

3. Statement: [tex]\( x < 0 \)[/tex]
- By definition, if [tex]\( x \)[/tex] is a negative number, then it is less than zero. So this statement is true.

4. Statement: [tex]\( -x > 0 \)[/tex]
- As we established earlier, if [tex]\( x \)[/tex] is negative, then [tex]\( -x \)[/tex] is positive. Positive numbers are greater than zero. Therefore, this statement is true.

Hence, when [tex]\( x \)[/tex] is a negative number, the statement that is false is:

[tex]\( -x \)[/tex] is to the left of zero.

Thus, the false statement is [tex]\( -x \)[/tex] is to the left of zero.
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