Comparing Absolute Values: Is -|-123| Equal to |+123|?

Question

Are the numbers opposite?

123,+123 -\left|-123\right|,\left|+123\right|

Step-by-Step Solution

The opposite of a number is what you add to a number to get zero. The opposite of a positive number is a negative number. And the opposite of a negative number is a positive number.

For instance, the opposite of the number 123123 is 123-123.

In this question, we are asked about 123-\left|-123\right| and +123\left|+123\right|.

The absolute value of any number, whether positive or negative, is its distance from zero on the number line, without considering the direction. Thus, +123=123\left|+123\right| = 123 and 123=123\left|-123\right| = 123.

Therefore, 123=123-\left|-123\right| = -123 and +123=123+\left|123\right| = 123.

Since 123-123 is indeed the opposite of +123+123, the correct answer is Yes.

Answer

Yes