What is the solution set of |–x| = –10?

|a| = b gives
a =b or a = -b

so,
|-x| = -10
gives
-x = -10 or -x = 10
x = 10, -10

now let us verify,
when x = 10, |-10| = +10 and it is not = -10
so, x= 10 is NOT a solution.

when x = -10, |-(-10)| = |10| = 10 and it is not = -10
so, x= -10 is NOT a solution.

hence, this equation does not have a solution.

If we know that |...| can never be negative, we can directly deduce that this equation does not have any solution.

(-0, -7) is your answer