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To find out which number is the farthest from -2 on the number line, we need more information, specifically we need to know the range of numbers we are considering. Without additional information, such as boundaries or a set of numbers to choose from, we cannot determine which number is farthest from -2.
If we were given a set of numbers, we would compare their distances from -2 by evaluating the absolute value of the difference between each number and -2. The number with the largest absolute value from this subtraction would be the farthest from -2 on the number line.
If we presume you are asking which number is the farthest within all real numbers, theoretically, there is no single number that is farthest from -2, as the number line extends infinitely in both directions.
The number line is a visual representation of the set of all real numbers in order, with each point on the line corresponding to a particular number. Any positive or negative number, including fractions and irrational numbers, can be plotted on the number line.
The distance between two points (or numbers) on the number line is often represented by the absolute value of their difference. The concept of absolute value is like asking how far a number is from zero without considering the direction.
For example, the absolute value of both 3 and -3 is 3, because both numbers are three units away from 0. So if you were asked to find which of 3 or -5 is farther from -2, you would calculate the absolute value of their difference from -2:
For 3: |3 - (-2)| = |3 + 2| = |5| = 5 For -5: |-5 - (-2)| = |-5 + 2| = |-3| = 3
From this, you see that 3 is farther from -2 on the number line than -5 because 5 is greater than 3.
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The concept of "farthest" is not precise in this case without additional context because on the infinite number line, there is no limit to how far a number can be from -2. Numbers can go on infinitely in either direction. However, if we constrain the problem to a specific range of numbers or a given set of options, then we could identify which number is farthest from -2 within those constraints. If you can provide a specific set of numbers or a range to consider, I can identify the number that is farthest from -2 on the number line within that context.