Hello, The topic of the day is the **Linear inequalities** Chapter of **Class 11 Maths**. As given in **NCERT Class 11th Maths** Book, the **Linear inequalities Chapter** is the 6th chapter. As the name of the Chapter suggests that this chapter represent the inequality between different sources or problems. A **linear inequality** is an algebraic expression.

Generally, we had learned linear equations such as x + y = 0, 2x – 2 = y, etc in the previous class but in this chapter, you will learn new concepts. I mean to say that the equal sign of the above equation is replaced by the greater than sign(<) or smaller than sign(>) or much more. Like x + y > 0, 2x – 2 < y, etc.

## Linear Inequalities Class 11 NCERT Solutions

Let’s start to learn the “**what do you mean by Linear Inequalities Chapter of Class 11th Maths Book**?”

**Linear Inequalities** – It is a mathematical expression like an equation but it is different from a linear equation. As we know, If x + y = 20 then we say it is a linear equation but x + y > 20 then we say it is a Linear Inequalities. Let solve some questions in this chapter. Solve the following questions of the Linear inequalities Chapter of Class 11th Maths.

I describe with the help of two examples of different algebraic expressions. Let 25x + 2 = 177 and 25x + 2 < 200. Again, let it be statement 1 and statement 2. You can see both statements which are given above. Now, the point at this time is that statement 1 is an equation but statement 2 is not and statement 2 is an inequality. I hope you understand what is inequality or linear inequalities.

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### Linear Inequalities 11th Notes

- (i) Solve it 30x < 200, when x is a Natural Numbers and an Integer.
- (ii) Solve it 24x < 100, when x is a Natural Numbers and an Integer.
- (iii) Solve it 5x + 3 > 9, when x is a Natural Numbers and an Integer.
- (iv) Solve it 3y – 2 < 25, when x is a Natural Numbers and an Integer.

Follow these steps for getting the answers to questions of the **Linear inequalities** Chapter of **Class 11 Maths** NCERT Exercise 6.1 Solutions.

**(i) Solve it 30x < 200, when x is a Natural Numbers and an Integer.**

First of all, we should divide it by 30 because when we divide it by 30, we got the x value. When we divide 30x < 200 by 30, we got x < 20/3.

Case (1):- when x is a Natural number so the value of x is 1, 2, 3, 4, 5 and 6.

Case (2):- when x is an integer so the value of x is ( …., -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6).

**(ii) Determine it 24x < 100 when x is a Natural Numbers and an Integer.**

First of all, we should divide it by 24 because when we divide it by 24, we got the x value. When we divide 24x < 100 by 24, we got x < 25/6.

Case (1):- when x is a Natural number so the value of x is 1, 2, 3 and 4.

Case (2):- when x is an integer so the value of x is ( …., -4, -3, -2, -1, 0, 1, 2, 3, 4).

#### Linear Inequalities Class 11 Notes Pdf NCERT Solutions

Now, we will learn the types of inequality or linear inequalities. Let’s start to learn from inequality. What is inequality in brief means How can I define that it is inequality or not? The Chapter Solution of Linear Inequalities Class 11 of NCERT Book is are following:-

**(2) Get the solution of -12x > 30, when (i) x is a natural number (ii) x is an integer number.**

First of all, we should divide it by -12 because when we divide it by -12, we got the x value. When we divide -12x > 30 by -12, we got x < -5/2.

Case (1):- when x is a natural number. The value of x is nothing.

Case (2):- when x is an integer so the value of x is ( …., -4, -3).

**(3) Get the solution of 5x-3 < 7, when (i) x is a integer number (ii) x is an real number.**

First of all, add 3 on both sides then divide them by 5 because when we divide it by 5, we got the x value. When we add 3 on both sides, we get 5x < 10 and divide it by 5, we get x < 2.

Case (1):- when x is an integer number. The value of x is ( …., -4, -3, -2, -1, 0, 1).

Case (2):- when x is a real number. The value of x is (-∞, 2) except 2.

**(4) Get the solution of 3x + 8 > 2, when (i) x is a integer number (ii) x is an real number.**

First of all, subtract 8 on both sides then divide them by 3 because when we divide it by 3, we got the x value. When we subtract 8 on both sides, we get 3x > -6 and divide it by 3, we get x > -2.

Case (1):- when x is an integer number. The value of x is (-1, 0, 1, ….).

Case (2):- when x is a real number. The value of x is (-2, ∞) except -2.