Question

What is the solution set of -x]=-10?

Answer 1

Explanation:

|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.