When we find the solution set of inequality, we need to domain of the variable and then write the possible solutions of the inequality.

### Solved Examples

**Question 1: **Find the solution set of the equation: 3 ( x- 4 ) = 2 ( 9 - x)

** Solution: **

We have 3 ( x - 4 ) = 2 ( 9 - x )

=> 3 . x - 3(4) = 2(9) - 2 . x

=> 3 x - 12 = 18 - 2 x

=> 3 x + 2 x = 18 + 12

=> 5x = 30

=> x = $\frac{30}{5}$

= 6

** The solution set is x = { 6 }**

**Question 2: **Write the solution set of x $\le$ 5, and x $\epsilon$ N

** Solution: **

The domain consists of Natural numbers and the inequality is x less than or equal to 5

( i. e ) N = { 1, 2, 3, 4, 5,. . . . . }

The natural numbers less than or equal to 5 are 1, 2, 3, 4 and 5.

Therefore,** The solution set is x = { 1, 2, 3, 4, 5 }**

**Question 3: **Write the solution set of x > - 4 and x $\epsilon$ Z.

** Solution: **

The domain consists of Integers and the inequality is x greater than - 4

( i. e ) Z = { . . . . . . - 4, -3, -2, -1, 0 , 1, 2, 3, 4 . . . . . . .}

The integers greater than -4 are , -3, -2, -1, 0, 1, 2, 3, 4, . . . . . . . . .

Therefore,** the solution set is { -3, -2, -1, 0, 1, 2, 3, 4, . . . . . . . . . }**

**Question 4: **Write the solution set of -2 < x $\le$ 10 and x $\epsilon$ W

** Solution: **

We have -2 < x $\le$ 10

The domain of x is set of whole numbers.

( i. e ) W = { 0, 1, 2, 3, 4, . . . . . . . . .}

The
whole numbers greater than -2 and less than or equal to 10 are, 0, 1,
2, 3, 4, 5, 6, 7, 8, 9, 10 since the whole numbers cannot be negative (
whole numbers are non-negative).

**The solution set is { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }**