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Q: What numbers have equal absolute values?

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The sum of the absolute values of two numbers is greater or equal than the absolute values of the sum. It will be equal if both are positive or both are negative; greater if one is positive and one is negative. Try it out with some sample numbers!

All numbers have opposites that are the same as their absolute values.

Consider the absolute values (the numerical values ignoring the signs) of the two numbers. If these are equal then the sum is equal; otherwise the sum takes the sign of which ever number has the larger absolute value.

never

No. Absolute value applies to the set of real numbers.

no all absolute values are positive

You can compare their magnitude (absolute values) but not the numbers themselves.

NO! abs(2-2)=0 NOT equal to abs(2)+abs(-2)=4 - The above is technically correct, though the more thorough answer is as follows; no because the absolute value of the sum is LESS THEN OR EQUAL TO the sum of the absolute values. The simple proof the the fact that |A+B|<=|A|+|B| is called the triangular inequality. When A and B (or for that matter an infinite number of them) are both positive (or all) or both negative (or all) then they inequality is actually equal, if however any of the numbers have different signs then any other number, the inequality is less then.

yes

An integer that is equal in magnitude to the sum of their absolute values. Its sign is the same as which of the two numbers you are taking the difference from. For example, for the integers 5 and -7. Their absolute values are 5 and 7 so that the sum of the absolute values is 5+7 = 12. Then 5 - (-7) = +12 and -7 - 5 = -12.

The absolute value of the sum of two complex numbers is less than or equal to the sum of their absolute values.

on the real number line there are 2 values with |5|, ie +5 and -5. on the complex plane there are an infinite set of values with an absolute value of 5, ie all the points of distance 5 from the origin.

The absolute value (|5|) numbers are 5 and -5.

yes

It means that you take the absolute values of different numbers, and then compare them to see which one is greater.

The additive opposite is negative 8 (-8). Absolute values are always positive numbers.

Ah! but they can. Using absolute values |3-i|<|3+2i|.

Absolute value

The value of the answer is the sum of the absolute values of the numbers and the sign of the answer is the same as that of the two numbers.

Numbers have unique values. Consequently, only 150000 has the value 150000.

It gets the average of the absolute deviations of a set of values from their mean. It can use numbers or references to those numbers.

The sum of two negative numbers is positive and the sum of two negatives is negative. If you have both positive and negative numbers the sum can be either so look at the absolute value. If the negative number has a greater absolute value, the sum is negative. If the positive number has a greater absolute value the sum is positive. If the absolute values are equal, the sum is zero.

The absolute value of the answer is the difference between the absolute values of the two numbers and the sign associated with it is the same as that of the number with the greater absolute value.

This is not strictly true, because an absolute value, and hence the product of two absolute values can be zero. It is, therefore true to say that the product of two absolute values is always non-negative. An absolute value of a number is, by definition, non-negative. And by the definition of multiplication, the product of two non-negative numbers in non-negative.

absolute is equal to guage pressur plus atmospheric