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Linear Inequalities

Short Answer Type

61. Represent the following inequality graphically in two dimensional plane:
2x + 6 > 0

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62. Represent the following inequality graphically in two dimensional plane:
3y + 6 < 0

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63. Solve the following inequality graphically in two-dimensional plane:

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64. Solve the following inequality graphically in two-dimensional plane:

4 straight x minus 3 straight y greater or equal than 0

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65. Solve the following inequality graphically in two-dimensional plane:
x + y < 5

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66. Solve the following inequality graphically in two-dimensional plane:

space space straight x space minus space straight y space greater or equal than space 2

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67.

Solve the following inequality graphically in two-dimensional plane:
– 3x + 2y ≥ – 6

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68.
Solve the following inequality graphically in two-dimensional plane:
3y – 5x < 30

First, we draw the dotted line to represent the graph of straight line 3y - 5x = 30
x 0 -6
y 10 0

Now, let us take a point O(0, 0) i.e, origin.
Substitute in given inequality, 3(0) - 5(0) < 30 or 0 < 30 which is true. Therefore, origin O(0, 0) is the solution of given inequality. From these observations, the graph is given ahead in which shaded region represents the solution of the given inequality.