The value of the expressions (6 + 3) and (6 × 3) are 9 and 18 respectively.

__Inequality__

The
value of the expressions (6 + 3) and (6 × 3) are 9 and 18 respectively.

It
means the above two expressions are not equal.

We
can consider another example. Take two numbers 4 and 5. We know that 4 is not
equal to 5. But, still we can relate those two numbers by a relationship.

If
two expressions or numbers are not equal, one of them is greater or smaller
than the other. To show ‘greater than’ and ‘lesser than’, we use the symbols
‘>’ and ‘<’ respectively.

This
kind of representation is called an ‘inequality’.

Let
us consider another example, the value of (9 − 5) is 4 and the value of (25 ÷
5) is 5 and we know that 4 < 5. So, the relation between the expressions (9 −
5) and (25 ÷ 5) can be shown as (9 − 5) < (25 ÷ 5).

**Note:** In your higher class
you will learn about two more inequalities, that is ‘≥‘ and ‘≤‘. These, two
symbols can be read as, greater than or equal to (≥) and lesser than or equal
to (≤).

** **

__Example 4.2__

Fill
in the boxes between the expressions with <, = or > as required in the
following.

**i) (7 +8 ) **** (20÷2)**

**Solution**

First,
we have to add 7 and 8

7+8
= 15,

Now,
we divide 20 by 2, we get

20
÷ 2=10

Therefore,
(7+8) (20 ÷ 2)

15
> 10

Hence,
(7 +8) > (20 ÷ 2)

**ii)
(12 × 3) (9 ****× 4)**

**Solution**

First,
we have to multiple 12 by 3

12
× 3 = 36

Now,
multiplying 9 by 4 we get,

9
× 4 = 36,

Since,
(12 × 3) and (9 × 4) is equal, we have,

(12
× 3) = (9 × 4)

**iii) (15−5) **** (8** **×
3)**

**Solution**

First,
we have to subtract 5 from 15.

15−5=10

Now,
multiplying 8 by 3, we get,

8
× 3 = 24

Since,
(15 − 5 = 10) is less than (8 × 3 = 21), we have,

(15 − 5) < (8 × 3).

__Example 4.2__

Write
a number in the box that will make this statements correct.

i. (6 × 4) = ( −6)

**Solution**

The
value of the expression 6 ×
4 is 24. So, the number in the box has to be one that gives 24 when 6 is
subtracted from it. Subtracting 6 from 30 gives 24.

Therefore,
(6 × 4) = (** 30**−6)

ii)
(35÷5) < (2+)

**Solution**

The
value of the expression 35 ÷ 5 is 7. So, the number in the box has to be such
that when it is added to 2, the sum is greater than 7.

Therefore,
(35 ÷ 5) < ( 2 + ** 6** )

Instead of 6, the solution for this condition
can be 7, 8,....

Tags : Algebra | Term 3 Chapter 4 | 5th Maths , 5th Maths : Term 3 Unit 4 : Algebra

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5th Maths : Term 3 Unit 4 : Algebra : Inequality | Algebra | Term 3 Chapter 4 | 5th Maths

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