If the absolute values of two rational numbers are equal, then the two numbers are mutually opposite. Right?

Of course not.
Two numbers can be the same, like five and five.

If the absolute value of a rational number is 3 and the opposite number of another rational number is -4, what is the sum of the two rational numbers?

The absolute value of a rational number is 3,
The rational number is 3 or -3;
The opposite of another rational number is -4,
The other rational number is 4,
Then 3+4=7 or (-3)+4=1, i.e. the sum of the two rational numbers is 7 or 1.

RELATED INFORMATIONS

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