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Q: If x is a rational number and y is the opposite of x why do x and y have the same absolute value?

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how do you identify opposite and absolute value of a rational number

The absolute value is always positive.

The opposite of any rational number, q is -q. Then if q >= 0 , its opposite and absolute value are both q.If q < 0 then -q > 0 and the opposite and absolute value are both -q.

The opposite of the absolute value of x is always -abs(x).

When the number is 0.

The additive opposite of the rational number q is -q. One of q and -q must be non-negative and that is its absolute value.

It would be a positive or negative number

They are all non-positive rational numbers.

It is the number with the same magnitude (absolute value) and the opposite sign.

When the number is non-positive.

Suppose x is a rational number -x is the [additive] opposite of x.If x < 0 then -x > 0 so that the absolute value is -x (if x is negative then -x is positive).if x >= 0 then the absolute value is x.

I would do it that way.

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