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**HallsofIvy** To say that "x is at least 6 units from 4" means that x must be larger than x= 4+ 6= 10 or smaller than x= 4- 6= -2. That "x= 4+ 6" is the same as "x- 4= 6" and "x= 4- 6" is the same as "x- 4= -6" so we are saying that x- 4> 6 or that x- 4< -6. Both cases can be expressed as |x- 4|> 6.

Your "|x- 6|> 4" is wrong because x= 1 satisfies |1- 6|= 5> 4, but the distance from x= 1 to 4 is 3 which is NOT greater than 6. "|x- 6|> 4" is satisfied by all x whose distance from **6** is greater than **4**, not the other way around.

Remember that, in general, the distance between points "a" and "b", on the number line, is |a- b|. So, here, the distance of x "from 4" is |x- 4|.