Answer :
To solve the equation [tex]\( |x| = -7 \)[/tex], it's important to understand what the absolute value symbol means. The absolute value of a number, denoted by [tex]\( |x| \)[/tex], represents the distance of that number from 0 on the number line. This distance is always non-negative. Therefore, the absolute value of any number is always zero or positive, never negative.
In this problem, we are asked to find the values of [tex]\( x \)[/tex] such that [tex]\( |x| = -7 \)[/tex]. Since the absolute value can never be negative, it is impossible for [tex]\( |x| \)[/tex] to equal [tex]\(-7\)[/tex].
Therefore, there are no values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( |x| = -7 \)[/tex]. The correct answer is option F: None.
In this problem, we are asked to find the values of [tex]\( x \)[/tex] such that [tex]\( |x| = -7 \)[/tex]. Since the absolute value can never be negative, it is impossible for [tex]\( |x| \)[/tex] to equal [tex]\(-7\)[/tex].
Therefore, there are no values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( |x| = -7 \)[/tex]. The correct answer is option F: None.
