Class 11 Maths Linear Inequalities Solution for linear inequality in one variable

Solution for linear inequality in one variable

Solution & Solution Set

Solution: Values of x, which make inequality a true statement. E.g. 3 is a solution for x<7

Solution Set: The set of values of x is called its solution set. E.g.: 1,2,3,4,5,6 is solution set for x<7   where x is natural Number Rules of Inequality:

• Equal numbers may be added to (or subtracted from) both sides of an inequality without affecting the sign of inequality. E.g. x<7 is same as x +2 <7+ 2
• Both sides of an inequality can be multiplied (or divided) by the same positive number without affecting the sign of inequality. E.g. : x+y <7 is same as (x+y) *3 < 7 * 3
• But when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed g. : x+y <7     is same as  (x+y) *(-3)  >  7 *(- 3)

Numerical: Solve 30 x < 160 when (i) x is a natural number, (ii) x is an integer, (iii) x is real number

Solution:  Dividing the inequality by 30 as per rule 2.

30/30 x < 160/30

Or x< 16/3

Case 1: X is a natural number. Then solution set is {1,2,3,4,5}

Case 2: X is an integer.  Then solution set is {……-4,-3,-32,-1,0,1,2,3,4,5}

Case 3: X is a real number. Then solution set is (–∞,16/3).

We can represent case 3 solution using number line Numerical: Solve 7x + 2 ≤ 5x + 8. Show the graph of the solutions on number line.

Solution:  Subtracting 2 from both side we get

7x  ≤ 5x + 6

Subtracting 5x from both side we get

2x  ≤ 6

Dividing 2 both side we get

x  ≤ 3

We can represent this in Number line below. .