Question 204034
For the equation |m-2|>1,
would I solve it like so: |m-2| > 1 or |m-2| > -1<br>
Pretty close. To solve for "m" we need to get rid of the absolute value. And to do this correctly for your problem we replace |m-2|>1 with:
m-2 > 1 or m-2 < -1
(Note there are no absolute value anymore.) Now we solve these simple inequalities by adding 2 to both sides of both:
m > 3 or m < 1
This is your solution.<br>
or do i have to flip the inequality sign when i add the negative?
The only time to flip an inequality because of some arithmetic you are doing is when you multiply or divide (never for adding or subtracting) both sides of the inequality by any negative number. At no point in this problem is this being done. So you should not flip the inequality.<br>
Note that the first step of the problem involved changing the absolute inequality into a pair of simple inequalities (without absolute value). One of these two inequalities, the one with the opposite sign on the number, is always the opposite to the original inequality. This "flip" is just part of the process of getting rid of the absolute value.