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

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**Question 15:**

Fill in the blanks in the following:

**Answer:**

(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 _______

**Answer:**

(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

**Short Answer Type**

Solve for , the inequalities in Exercises 1 to 12.

**Question 1:**

**Answer:**

**Question 2:**

**Answer:**

**Question 3:**

**Answer:**

**Question 4:**

**Answer:**

**Question 5:**

**Answer:**

**Question 6:**

**Answer:**

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?

**Answer:**

More than

**Question 8:**

The water acidity in a pool is considered normal when the average pH reading of three daily measurements is between and . If the first two readings are and , find the range of value for the third reading that will result in the acidity level being normal.

**Answer:**

Between and