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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

First, we draw the dark line to represent the graph of straight line -3x + 2y = -6
x 0 2
y -3 0

Now, let us take a point O(0, 0), i.e., origin.
Substitute in given inequality, -3(0) + 2(0) ≥ -6, i.e., 0 ≥ -6 which is true. Therefore, origin O(0, 0) is solution of given inequality. From these observations, the graph is given below, in which the shaded region represents the solution of the given inequality.