Question 997081
your absolute value inequality will be |x - 2| > 5


when (x-2) is positive, the inequality becomes (x - 2) > 5.


add 2 to both sides of thsi inequality to get x > 7.


when (x-2) is negative, you flip the sign of the expression on the right and you slip the inequality sign to get (x - 2) < - 5.


add 2 to both sides of this inequality to get x < -3


your solution would then be that x > 7 and x < -3.


when x = 8 which is greater than 7, |x-2| > 5 becomes |8-2| > 5 which becomes |6| > 5 which becomes 6 > 5 which is true.


when x = -4 which is less than -3, |x-2| > 5 becomes |-4-2| > 5 which becomes |-6| > 5 which becomes 6 > 5 which is true.


the solution is confirmed to be good.