Cheesebig40idn
Answered

Experience the power of community-driven knowledge on IDNLearn.com. Ask anything and receive prompt, well-informed answers from our community of knowledgeable experts.

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 :

GinnyAnsweridn
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.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.