Question

The equation |x|=a has no solution if a is a negative number. (1 point) A. The statement is false. The equation |x|=a has one solution if a is a positive number. B. The statement is false. The equation |x|=a has one solution if a is a negative number. C. The statement is false. The equation |x|=a has no solution if a is a positive number. D. The statement is true.

Answer 1

The statement is false. The equation |x|=a has one solution if a is a negative number.

Explanation:

Given the expression |x|=a, we must understand that |x| can return both positive and negative value of x i.e

x=a and -x = a

from the second equation,

-x = a

multiply both sides by minus

-(-x) = a

x = -a

Hence If "a" is negative number according to the question then the equation has one solution which renders the fact that the equation has no solution if a is negative false.