In this article, we are going to learn about the meaning of absolute value, the symbol of absolute value, and the properties of absolute value. The absolute value of a number or integer is the distance of the number from zero, in a number line irrespective of the direction.
It is the distance from 0 and is expressed as a positive integer. The symbol used to represent an absolute value are vertical bars, i. The distance on the number line from the origin is always a non-negative quantity.
For example: the absolute value of 4 is written as 4 and the absolute of -4 is also written as 4. The following figure represents the absolute value of the integer 4 from the origin 0 on a number line. Irrespective of the direction, the absolute value of the integer is always positive. To represent the absolute value of a number x or a variable , we write a vertical bar on either side of the number, i. The word modulus is a Latin word that means measure. Since the absolute value is the distance of a number from the origin it can show both negative and positive numbers.
If the integer is positive then the absolute value will be a positive number. If the number is negative, even then the absolute value of this number will be a positive number. For example, the absolute value of 7 is written as 7 and the absolute value of -7 is written as This means that the absolute value of any number can never be negative because the distance is never represented in a negative form.
The following figure represents how the absolute value is the same for the positive and negative numbers. The graph of the absolute value function is shown below. The v-shaped line represents the distance between both the x-axis and y-axis. The absolute value function is used to measure the distance between two numbers. Example 1: Megan wants to find the values of the following.
Can you help her using the definition of absolute value? Example 2: Mia is instructed by her teacher to solve the following absolute value equation using the definition of the absolute function. Using the definition of the absolute value function, we remove the absolute value sign on one side of the equation.
This results in two equations, which we solve separately. The absolute value of a number or integer is the distance of the given number from zero, in a number line, irrespective of the direction. Later we will discuss graphs of absolute value equations and inequalities.
Absolute Value is a funny concept in Math that a lot of people have a hard time getting used to but the important thing to keep in mind when you're working with Absolute Value is to remember that Absolute Value just means distance away from zero, I'm going to say that lots of time. So like for example if I were looking at a problem that looks like this where it said "the Absolute Value of x equals 2.
That's the important thing to keep in mind it's just like distance away from zero. It's actually really useful in the real world you know how sometimes people say "where I'm I going to use this? Like if I'm on 10th and you're 5 blocks away, are you on 5th Avenue? Or are you on 15th? That's the way Absolute Value works, and it's pretty useful.
Also lot of times Absolute Value is used in manufacturing like if I already look at this bag of chips it tells me that the weight is Like there's an Absolute Value that's around this It might be actually higher than I might have got like my chip stolen out of my bag or something but the important thing when they're producing chips is they say okay all of our bags needs to be within a distance of maybe like 0.
It's how they set up like some are going to be more some are going to be less. So when you're looking at Absolute Value problems, keep in mind you're probably going to have more than one answer most of the time you'll have two answers, sometimes you'll have one answer and sometimes you'll even have no answer and that's a situation where you have an Absolute Value is equal to a negative number and you'll start seeing those when you get into your homework problems.
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