Question

Question 2 Solve –12x > 30, when

(i) x is a natural number

(ii) x is an integer

Class X1 - Maths -Linear Inequalities Page 122

Answer 1

★ LINEAR INEQUALITIES ★
REDUCING LINEAR INEQUALITIES AT THEIR MAXIMUM EXTENT HERE , AND IN OTHER FEW CASES ; GENERALITY HAS BEEN USED UPTO PROPER EXTENDS
AS BEING CAREFUL WHILE CHOOSING INTEGRAL SOLUTIONS OF THE RESPECTIVE INEQUALITY

★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★

Answer 2

(1) when x is natural number .
it means x is one of 1, 2 , 3 , 4 ......
e.g x is always positive number .
now,
-12x > 30
take both sides negative . from the rule of inequality sign change .
so, -(-12x) < -30
=> 12x < -30
divide by 12 both sides ,
=> x < -30/12
=> x < -2.5
there is no solution possible when x is natural number because less then -2.5 have no natural numbers .


(2) when x is integer .
it means x is one of 1, 2, 3 , .....0, -1 , -2 , -3 , ......
e.g x may be negative or positive.

now,
-12x > 30
=> 12x < -30
=> x < -30/12
=> x < -2.5
hence, x will be possible = { -3 , -4, -5 ,.....}