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The absolute value of the opposite of x is x.

The absolute value is the number's distance from zero on a number line. Distance can not be negative, so basically, to find the absolute value of a number you just need to make it positive.

The opposite of x is -x.

|-x|=x - you make the x positive

Of course, if x, to begin with, represents a negative (less than zero) number than the absolute value would be -x. For example if x=-3, the opposite value of x would be 3 and the absolute value of x would also be 3 which happens to be -x.

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