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Question 997081: Solve
Write an absolute value inequality representing all numbers that are at least 2 units from 5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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