# 28 Apr Absolute Values

At Miracle Learning Centre, we teach you interesting stuff in math tuition. In this maths tuition, we are going to talk about absolute values. A solid foundation of this concept is required in order to do well in math. As a result, we are going to learn about the basics of absolute values and also discuss some of their interesting properties. In order to understand the topics discussed here, you should already be familiar with equations and inequalities. Without any further delay, let us get started with this maths tuition.

Absolute value of any number is that number’s distance from 0 on the number line. Let us see with an example.

Consider the number -4 on the number line below.

4

3

2

1

-1

-2

-3

-4

0

As you can see, the distance of -4 from 0 is 4. As a result, the absolute value of -4 is 4. Similarly, the absolute value of 4 as well is 4.

The absolute value of any number is positive since it is the distance of the number from 0 and distance is always positive. For example, absolute value of -6 is 6, absolute value of -10 is 10 , absolute value of 12 is 12 etc.

The mathematical way to express absolute value is |x| where x is any number.

For example,

|-6| = 6

|-10| = 10

|100| = 100

**Equations involving absolute value**

In this section of this math tuition, we are going to see some properties of those equations which involve absolute value.

Consider the following equation for example:

|x| = 5

For the above equation, value of x could be 5 or -5 and both will satisfy the equation. So we can conclude from the above equation that :

x = 5 or -5

Now, let us consider the following equation:

|x – 7| = 11

If we remove the absolute value sign, the equation becomes:

x-7 = – 11 or x-7=11

Solving for each of the above equations, we get:

x = -4 or x = 18

So, we can see that in case of the above equation, x can take two values – 4 or 18 and both will satisfy the equation.

**Absolute value and inequality**

In this section of this math tuition, we are going to see how inequalities involving absolute values behave. Many beginners find it confusing to deal with such equations and as a result, we are going to touch upon the basics and develop a solid understanding of the concept.

Consider the following equation where it is given that x is an integer and:

|x| < 5

For the above equation, x can take the following values(since we are told that x is an integer, it cannot take decimal values):

-4,-3,-2,-1,0,1,2,3,4

Let us see why. First, consider the case when x=5. In this case, |x| = 5. However, the equation clearly states that the value of |x| is less than 5. So x cannot take a value greater than or equal to 5. So the upper bound for x is 4 since we are told that x is an integer.

On the other hand, when x = -5, |x| = 5. As a result, x cannot be less than or equal to -5.So the lower bound for x is -4.

So, in the language of mathematics:

-5 < x < 5

In this math tuition, we learned about absolute values and got familiar with equations which involve absolute values. It is important that you understand the concept of absolute values in order to do well in algebra and in math on the whole. In case you find any difficulty in understanding the ideas discussed above, do not hesitate to talk to your friends or your teacher at math tuition. We hope you enjoyed this math tuition from Miracle Learning Centre. Look out for the next math tuition from Miracle Learning Centre.