# NCERT Class 11-Math's: Chapter –6 Linear Inequalities Part 5

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Question 15:

Fill in the blanks in the following:

(i) If , then _____________ 2

(ii) If , then ____________

(iii) If , then _________ __________

(iv) If and , then

(v) If , then ____________

(vi) If , then _______ or __________

(vii) If and , then _______

(i) , because same number can be added to both sides of inequality without changing the sign of inequality.

(ii) , after multiplying both sides by , the sign of inequality is reversed.

(iii) , because if and , then

(iv) , if both sides are divided by the same negative quantity, then the sign of

(v) .

(vi)

(vii), as is positive and is negative, therefore, is always smaller than .

## 6.3 EXERCISE

Solve for , the inequalities in Exercises 1 to 12.

Question 1:

Question 2:

Question 3:

Question 4:

Question 5:

Question 6:

Given,

Also,

As and are not possible together.

So, has no solution.

Question 7:

A company manufactures cassettes. Its cost and revenue functions are and , respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?