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