Binomial Theorem


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


First, we draw the dotted line to represent the graph of x + y = 5
x       0        5
y       5        0
Now, let us take a point O(0, 0)
Substitute in given inequality, 0 + 0 < 5, i.e., 0 < 5 which is true.
Therefore, origin O is a solution of given inequality.
From these observations, the graph is given below, in which the shaded portion represents the solution of the given inequality which contains O(0, 0).

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