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.

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