# Exercise 6.2(Linear Inequalities )

Solve the following inequalities graphically in two-dimensional plane:(Ex 6.2 Linear Inequalities ncert math solution class 11)

Question 1: x + y < 5

Solution: Given that

 x 0 5 y 5 0

Now, draw a dotted line x + y = 5 in the graph

Now, consider x + y < 5

Select a point (0, 0).

â‡’Â 0 + 0 < 5

â‡’Â 0 < 5 (this is true)

âˆ´ 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:

Question 2: 2x + y â‰¥ 6

Solution : Given that: 2x + y â‰¥ 6

 x 0 3 y 6 0

Now, draw a solid line 2x + y = 6 in the graph

Now, consider 2x + y â‰¥6

Select a point (0, 0).

â‡’Â 2 Ã— (0) + 0 â‰¥Â 6

â‡’ 0 â‰¥ 6 (This is false.)

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

The graph is as follows:

Question 3: 3x + 4y â‰¤ 12

Solution: Given that, 3x + 4y â‰¤ 12

 x 0 4 y 3 0

Now, draw a solid line 3x + 4y = 12 in the graph

Now, consider 3x + 4y â‰¤ 12

Select a point (0, 0).

â‡’Â 3 Ã— (0) + 4 Ã— (0)Â â‰¤ 12

â‡’ 0 â‰¤ 12 (This is true.)

âˆ´ 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:

Question 4: y + 8 â‰¥ 2x

Solution: Given that, y + 8 â‰¥ 2x

 x 0 4 y -8 0

Now, draw a solid line y + 8 = 2x in the graph

Now, consider y + 8 â‰¥ 2x

Select a point (0, 0).

â‡’Â (0) + 8Â â‰¥Â 2 Ã— (0)

â‡’ 0â‰¤ 8 (This is true.)

âˆ´ 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:

Question 5: x â€“ y â‰¤ 2

Solution: Given that, x â€“ y â‰¤ 2

 x 0 2 y -2 0

Now, draw a solid line x â€“ y = 2 in the graph

Now, consider x â€“ y â‰¤ 2

Select a point (0, 0).

â‡’Â (0) â€“ (0) â‰¤ 2

â‡’ 0 â‰¤ 2 (This is true.)

âˆ´ The solution region of the given inequality is above the line x â€“ y = 2. (That is, the origin is included in the region.)

The graph is as follows:

Question 6: 2x â€“ 3y > 6

Solution: Given that, 2x â€“ 3y > 6

Now, draw a dotted line 2x â€“ 3y = 6 in the graph

Now, consider 2x â€“ 3y > 6

Select a point (0, 0).

â‡’Â 2 Ã— (0) â€“ 3 Ã— (0) > 6

â‡’ 0 > 6 (This is false.)

âˆ´ The solution region of the given inequality is below the line 2x â€“ 3y > 6. (Away from the origin.)

The graph is as follows:

Question 7: â€“ 3x + 2y â‰¥ â€“ 6

Solution: Given that, â€“ 3x + 2y â‰¥ â€“ 6

Now, draw a solid line â€“ 3x + 2y = â€“ 6 in the graph

Now, consider â€“ 3x + 2y â‰¥ â€“ 6

Select a point (0, 0).

â‡’Â â€“ 3 Ã— (0) + 2 Ã— (0) â‰¥ â€“ 6

â‡’ 0 â‰¥ â€“ 6 (This is true.)

âˆ´ The solution region of the given inequality is above the line â€“ 3x + 2y â‰¥ â€“ 6. (That is, the origin

is included in the region)

The graph is as follows:

Question 8: 3y â€“ 5x < 30

Solution: Given that, y â€“ 5x < 30

 x 0 -6 y 10 0

Now, draw a dotted line 3y â€“ 5x = 30 in the graph

Now, consider 3y â€“ 5x < 30

Select a point (0, 0).

â‡’Â 3 Ã— (0) â€“ 5 Ã— (0) < 30

â‡’ 0 < 30 (This is true.)

âˆ´ The solution region of the given inequality is below the line 3y â€“ 5x < 30. (That is, the origin is included in the region.)

The graph is as follows:

Question 9: y < â€“ 2

Solution: Given that, y < â€“ 2

Now, draw a dotted line y = â€“ 2 in the graph

Now, consider y < â€“ 2

Select a point (0, 0).

â‡’ 0 < â€“ 2 (This is false)

âˆ´ The solution region of the given inequality is below the line y < â€“ 2. (That is, away from the origin.)

The graph is as follows:

Question 10: x > â€“ 3

Solution: Given that, x > â€“ 3

Now, draw a dotted line x = â€“ 3 in the graph

Now, consider x > â€“ 3

Select a point (0, 0).

â‡’Â 0 > â€“ 3

â‡’ 0 > â€“ 3 (This is true.)

âˆ´ The solution region of the given inequality is right to the line x > â€“ 3. (That is, the origin is included in the region.)

The graph is as follows:

Ex 6.1 Linear Inequalities ncert math solution class 11

Ex 6.2 Linear Inequalities ncert math solution class 11

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