Calculation:
Given: The absolute value of a number is equal to the absolute value of its opposite.
Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative. The absolute number of a number ais written as . The symbol is used to indicate the absolute value of a. is a, If ais positive. is a, if ais negative.
The equation = a has two solutions and because both numbers are at the distance a from 0.
1, A number and the opposite of the number always have the same absolute value.
2. In general, taking the opposite of n changes the sign of n.
For example, the opposite of 3 is -3.
3. In general, taking the absolute value of n gives a number , which is always positive. For example, and .
4, Since the opposite of 0 is 0 (which is neither positive nor negative), therefore -0 = 0. The number 0 is the only number which is its own opposite.
Conclusion:
The statement is true.