Answer:
only the first answer option is correct.
Explanation:
|-x - 4| = 8 has 2 solutions :
x = 4, x = -12 as |-8| = |8| = 8
this is correct.
3.4×|0.5x - 42.1| = -20.6 has no solution.
the left side is always a positive number for sure (product of a positive number and an absolute value, which is always a positive number). that can never be equal to a negative number.
|½x - 3/4| = 0 has exactly 1 solution.
x = 6/4
|2x - 10| = -20 has no solutions.
as in the second answer option, an absolute value is always a positive number and cannot be equal to a negative number.
|0.5x - 0.75| + 4.6 = 0.25 has no solutions.
as this is the same as
|0.5x - 0.75| = -4.35
as before, an absolute value is always positive and cannot be equal to a negative number.
|⅛x - 1| = 5 has exactly 2 solutions.
x = 48, x = -32 as |-5| = |5| = 5