Chapter 6: Linear Inequalities Exercise 6.2

Given, x + y < 5

Consider,

Now, draw a dotted line x + y = 5 in the graph (∵ x + y = 5 is excluded in the given question.)

Now, consider x + y < 5

Select a point (0, 0).

⇒ 0 + 0 < 5

⇒ 0 < 5 (this is true)

∴ The solution region of the given inequality is below the line x + y = 5. (That is, the origin is included in the region.)

The graph is as follows:

Given 2x + y ≥ 6

Now, draw a solid line 2x + y = 6 in the graph (∵ 2x + y = 6 is included in the given question.)

Now, consider 2x + y ≥6

Select a point (0, 0).

⇒ 2 × (0) + 0 ≥ 6

⇒ 0 ≥ 6 (This is false.)

∴ The solution region of the given inequality is above the line 2x + y = 6. (Away from the origin.)

The graph is as follows:

Given, 3x + 4y ≤ 12

Now, draw a solid line 3x + 4y = 12 in the graph (∵ 3x + 4y = 12 is included in the given question.)

Now, consider 3x + 4y ≤ 12

Select a point (0, 0).

⇒ 3 × (0) + 4 × (0) ≤ 12

⇒ 0 ≤ 12 (This is true.)

∴ The solution region of the given inequality is below the line 3x + 4y = 12. (That is, the origin is included in the region.)

The graph is as follows:

Given, y + 8 ≥ 2x

Now, draw a solid line y + 8 = 2x in the graph (∵ y + 8 = 2x is included in the given question.)

Now, consider y + 8 ≥ 2x

Select a point (0, 0).

⇒ (0) + 8 ≥ 2 × (0)

⇒ 0≤ 8 (This is true.)

∴ The solution region of the given inequality is above the line y + 8 = 2x. (That is, the origin is included in the region.)

The graph is as follows:

Given, x – y ≤ 2

Now, draw a solid line x – y = 2 in the graph (∵ x – y = 2 is included in the given question.)

Now, consider x – y ≤ 2

Select a point (0, 0).

⇒ (0) – (0) ≤ 2

⇒ 0 ≤ 2 (This is true.)

∴ The solution region of the given inequality is above the line x – y = 2. (That is, the origin is included in the region.)

The graph is as follows:

Given, 2x – 3y > 6

Now, draw a dotted line 2x – 3y = 6 in the graph (∵ 2x – 3y = 6 is excluded in the given question.)

Now, consider 2x – 3y > 6

Select a point (0, 0).

⇒ 2 × (0) – 3 × (0) > 6

⇒ 0 > 6 (This is false.)

∴ The solution region of the given inequality is below the line 2x – 3y > 6. (Away from the origin.)

The graph is as follows:

Given, – 3x + 2y ≥ – 6

Now, draw a solid line – 3x + 2y = – 6 in the graph (∵– 3x + 2y = – 6 is included in the given question.)

Now, consider – 3x + 2y ≥ – 6

Select a point (0, 0).

⇒ – 3 × (0) + 2 × (0) ≥ – 6

⇒ 0 ≥ – 6 (This is true.)

∴ The solution region of the given inequality is above the line – 3x + 2y ≥ – 6. (That is, the origin

is included in the region)

The graph is as follows:

Given, y – 5x < 30

Now, draw a dotted line 3y – 5x = 30 in the graph (∵3y – 5x = 30 is excluded in the given question.)

Now, consider 3y – 5x < 30

Select a point (0, 0).

⇒ 3 × (0) – 5 × (0) < 30

⇒ 0 < 30 (This is true.)

∴ The solution region of the given inequality is below the line 3y – 5x < 30. (That is, the origin is included in the region.)

The graph is as follows:

Given, y < – 2

Now, draw a dotted line y = – 2 in the graph (∵ y = – 2 is excluded in the given question.)

Now, consider y < – 2

Select a point (0, 0).

⇒ 0 < – 2 (This is false)

∴ The solution region of the given inequality is below the line y < – 2. (That is, away from the origin.)

The graph is as follows:

Given, x > – 3

Now, draw a dotted line x = – 3 in the graph (∵x = – 3 is excluded in the given question.)

Now, consider x > – 3

Select a point (0, 0).

⇒ 0 > – 3

⇒ 0 > – 3 (This is true.)

∴ The solution region of the given inequality is right to the line x > – 3. (That is, the origin is included in the region.)

The graph is as follows:

NCERT Class 11 Solutions for Maths Chapter 6 exercise wise problems can be referred by clicking on the links below.

Exercise 6.1 Solutions 26 Questions

Exercise 6.3 Solutions 15 Questions

Miscellaneous Exercise on Chapter 6 Solutions 14 Questions