What does it mean when two numbers have the same absolute value?

What does it mean when two numbers have the same absolute value?

opposites
Two numbers are opposites if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0. The opposite of 0 is 0.

What is always true about the absolute value of a number?

What Does Absolute Value Mean? Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Can two different numbers can have the same absolute value?

Answer: Two different integers can have the same absolute value.

What are two facts about absolute value?

Real numbers The absolute value of x is always either positive or zero, but never negative. From an analytic geometry point of view, the absolute value of a real number is that number’s distance from zero along the real number line. The absolute value of the difference of two real numbers is the distance between them.

Which pairs of numbers have the same absolute value How are these numbers related?

An integer and its opposite are the same distance from zero. So, they have the same absolute values because absolute value is the distance between the number and zero.

What has the same absolute value as?

The absolute value is the same as the distance from zero of a specific number. On this number line you can see that 3 and -3 are on the opposite sides of zero. Since they are the same distance from zero, though in opposite directions, in mathematics they have the same absolute value, in this case 3.

Is it true that an integer and its absolute value are always opposites?

Carl is right. An integer and its opposite are the same distance from zero. So, they have the same absolute values because absolute value is the distance between the number and zero.

Why do they have the same absolute value?

What is the absolute value of 2?

The absolute value is just the distance from the origin we can say that 2 is a distance of two units away from 0, but also that −2, the opposite of 2 (and on the other side of 0), is two units away from 0. So both 2 and −2 are two units away from 0.

What two values each have an absolute value of 5?

The absolute value of 5 is 5, it is the distance from 0, 5 units. The absolute value of -5 is 5 it is the distance from 0, 5 units.

Is the opposite of a number the same as the absolute value of a number?

A number and the opposite of the number always have the same absolute value. |−3| = 3. Since the opposite of 0 is 0 (which is neither positive nor negative), –0 = 0. The number 0 is the only number that is its own opposite.

Can two different numbers have the same absolute value?

Hence if domain is real number for each absolute value there are two different numbers one can have with same absolute value. However, if domain is Complex numbers, absolute value of a number a+bi is √a2+b2 and for each absolute value there could be infinite different numbers with same absolute value. For example, 3+4i, −4+3i,…

Why do absolute value equations have two solutions?

Because two numbers have the same absolute value (except 0 ). So |3x − 2| = 5 will have two solutions: One that makes 3x − 2 = 5 and another that makes 3x − 2 = − 5 (The solutions are 7 3 and −1 .)

When to use absolute value in real life?

Students use absolute value to find the magnitude of a positive or negative quantity in a real-world situation. What is the relationship between the following pairs of numbers? How do each pair of numbers relate to zero? What is the absolute value of a number?

How to calculate the absolute value of 10?

The absolute value of ten is written as |10|. On the number line, count the number of units from 10 to 0. How many units is 10 from 0? What other number has an absolute value of?