Introduction to Inequalities in Algebra

Introduction to Inequalities in Algebra

Welcome friends!

       Today we are going to learn a new thing called inequalities.

      Remember, mathematics is not always about “equals” or “equalities” sometimes we only know that something is greater than or less than other.

      Inequality tells us about the relative size of two values.

For example: Ajay is younger than Vijay

                    Ajay < Vijay

(I.e. Age of Ajay is less than age of Vijay Or

      Age of Vijay is greater than Ajay.)

Hence, we call it as “Inequality” (as they are not equal)

How to remember:

The “small” end always points to the smaller number.

Example: Only person with age 18 or greater can vote in India.

The “Inequality” is between person age and the age of 18

I.e. person with age 18 or greater can vote.

Solving Inequalities:

          This means we have to achieve (x< ….);(x > …..); (x£….); (x³…..) & we call that “solved”.

          Solving inequalities is very like solving equation…. We do most of the same thing.

Following things do not affect the direction of the inequality

·       Add or Subtract a number from both sides

·       Multiply or Divide a positive number from both sides.

·       Simplify only one side.

jkjFor Example

More examples:

Adding / subtracting on both sides works, because if we add/subtract same amount from both sides, it does not affect the inequality.

Following things do change the direction of inequality.

·       Multiply or Divide both sides by Negative number.

Swapping left and right hand sides.

As you swap the side, but reversing the sign so it still “Point at” the correct value.

Multiply or Dividing:

           You must be really careful while multiplying or dividing both sides of inequality.

Positive Number

Now Negative Number

When we multiply or divide by a Negative Number we must reverse the inequality.

How it works in Negative Number Multiplying or dividing

In Nutshell

1. Many Simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.

2. But, these things will change the direction of inequality.

·       Multiply or dividing both sides by a negative number.

·       Swapping left and right hand side of inequality.

 

Thank you! 

Hope you enjoyed it!!!