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Sagot :
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.
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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