NCERT Class 11-Math's: Chapter –6 Linear Inequalities Part 2

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Question 2:

Solve

Answer:

We have

and

or

or

Therefore, , i.e.

Question 3:

Solve

Answer:

We have

Question 4:

Solve .

Answer:

We have

and

Combining the solutions of two inequalities, we have

Question 5:

The cost and revenue functions of a product are given by and , respectively, where is the number of items produced and sold. How many items must be sold to realise some profit?

Answer:

We have,

To earn some profit,

Hence, the manufacturer must sell more than items to realise some profit.

Question 6:

Solve for .

Answer:

On LHS of the given inequality, we have two terms both containing modulus. By equating the expression within the modulus to zero, we get as critical points. These critical points divide the real line in three parts as .

Case I:

When

Case II:

When ,

(not possible)

Case III:

When ,

Combining the results of cases (I), (II) and (III), we get