Q1 of 65 Page 127

Solve the following inequalities graphically in two-dimensional plane:

x + y < 5

Given: x + y < 5

Consider: x + y = 5














X



0



5



Y



5



0



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)


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


The graph is as follows:



More from this chapter

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25

The longest side of a triangle is 3 times the shortest side and the third side is 2 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

 26

A man wants to cut three lengths from a single piece of board of length 91cm.

The second length is to be 3cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least 5cm longer than the second?


[Hint: If x is the length of the shortest board, then x, (x + 3) and 2x are the lengths of the second and third piece, respectively. Thus, x + (x + 3) + 2x 91 and 2x ≥ (x + 3) + 5].

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Solve the following inequalities graphically in two-dimensional plane:

3x + 4y ≤ 12