A) a negative number cannot equal a positive number , so A is not correct.
B) An absolute value is always positive, so it cannot equal a negative number, so B is not correct.
C is crossed out.
D) remove the absolute value term, by changing the -5 to both a positive and a negative 5 you then have X-2 = +/-5, which can be solved as X = 7, -3 which is what the dots on the line graph are above.
D is the correct answer.