Answer :
To solve the equation [tex]\( |x| = -7 \)[/tex], we need to understand the concept of absolute value.
The absolute value of a number, denoted as [tex]\( |x| \)[/tex], represents the distance of that number from zero on the number line. This distance is always a non-negative number. Therefore, the absolute value of any real number is always zero or positive; it can never be negative.
In the given equation [tex]\( |x| = -7 \)[/tex], we are asked to find the values of [tex]\( x \)[/tex] for which the absolute value equals [tex]\(-7\)[/tex]. Since the absolute value cannot be negative, it is impossible for any real number to have an absolute value of [tex]\(-7\)[/tex].
Thus, there are no solutions to the equation [tex]\( |x| = -7\)[/tex].
Looking at the given answer choices:
- A. 14
- B. 7
- C. -49
- D. 49
- E. -7
- F. None
None of these values can satisfy the equation because the equation itself has no real solutions. Therefore, the correct choice is:
- F. None
The absolute value of a number, denoted as [tex]\( |x| \)[/tex], represents the distance of that number from zero on the number line. This distance is always a non-negative number. Therefore, the absolute value of any real number is always zero or positive; it can never be negative.
In the given equation [tex]\( |x| = -7 \)[/tex], we are asked to find the values of [tex]\( x \)[/tex] for which the absolute value equals [tex]\(-7\)[/tex]. Since the absolute value cannot be negative, it is impossible for any real number to have an absolute value of [tex]\(-7\)[/tex].
Thus, there are no solutions to the equation [tex]\( |x| = -7\)[/tex].
Looking at the given answer choices:
- A. 14
- B. 7
- C. -49
- D. 49
- E. -7
- F. None
None of these values can satisfy the equation because the equation itself has no real solutions. Therefore, the correct choice is:
- F. None
