# NCERT Class 11-Math's: Chapter –6 Linear Inequalities Part 3

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## Long Answer Type

**Question 7:**

Solve for ,

**Answer:**

We have

Now two cases arise:

**Case I:** When . Then

**Case II:** When , i.e.,

it is not possible.

Combining (I) and (II), the required solution is

**Question 8:**

Solve the following system of inequalities:

**Answer:**

From the first inequality, we have

From the second inequality, we have

Note that the common solution of (1) and (2) is null set. Hence, the given system of inequalities has no solution.

**Question 9:**

Find the linear inequalities for which the shaded region in the given figure is the solution set.

**Answer:**

(i) Consider . We observe that the shaded region and the origin lie on opposite side of this line and satisfies . Therefore, we must have as linear inequality corresponding to the line .

(ii) Consider . We observe that the shaded region and the origin lie on the same side of this line and satisfies . Therefore, is the linear inequality corresponding to the line .

(iii) Consider . It is clear from the figure that the shaded region and the origin lie on the same side of this line and satisfies the inequality . Therefore, is the inequality corresponding to the line .

(iv) Consider . It may be noted that the shaded portion and origin lie on the same side of this line and satisfies . Therefore, is the inequality corresponding to the line .

(v) Also the shaded region lies in the first quadrant only. Therefore, .

Hence, in view of (i), (ii), (iii), (iv) and (v) above, the linear inequalities corresponding to the given solution set are:

.