Answer :
To solve the equation
[tex]$$
|x| = -7,
$$[/tex]
we first recall that the absolute value of any real number is always nonnegative. That is, for every real number [tex]$x$[/tex], we have
[tex]$$
|x| \geq 0.
$$[/tex]
Since [tex]$-7$[/tex] is a negative number, it is impossible for [tex]$|x|$[/tex] to equal [tex]$-7$[/tex]. Therefore, the equation has no solutions.
Thus, the correct answer is:
[tex]$$\text{None.}$$[/tex]
[tex]$$
|x| = -7,
$$[/tex]
we first recall that the absolute value of any real number is always nonnegative. That is, for every real number [tex]$x$[/tex], we have
[tex]$$
|x| \geq 0.
$$[/tex]
Since [tex]$-7$[/tex] is a negative number, it is impossible for [tex]$|x|$[/tex] to equal [tex]$-7$[/tex]. Therefore, the equation has no solutions.
Thus, the correct answer is:
[tex]$$\text{None.}$$[/tex]
