CPT Chapter Inequalities

With Anand.Duration:2hrs28min

What are inequalities?
Properties of inequalities
Solving inequalities
Drawing graph
Forming Signs from graph
Forming equations

What are Inequalities?

Example-
Tarun’s bag has less than 10 mangoes
Vinay saw not less than 10 tigers
Dylan earns not more than Rs 1,00,000
X is a whole number not more than 5
X is a real number not more than 5

Properties of Inequalities?
Common Properties-
Subtracting/adding same number on both sides of inequality does not alter it.
2x+6< 3(x-5)

Division/Multiplication by a positive number does not alter inequation

Division/Multiplication by a negative number changes inequation

Summary Common Properties-

Subtracting/adding same
Division/Multiplication by a positive number
Division/Multiplication by a negative number
Reciprocal relationship

Examples-

Find the range of real values of x satisfying the inequalities 3x - 2 > 7 and 4x - 13 > 15
a) x > 3
b) x > 7
c) x < 7
d) x < 3

On solving the inequalities 6x + y ≥18, x + 4y ≥ 12,
2x + y ≥10, we get the following situation :
a) (0,18), (12, 0), (4, 2) & (7, 6)
b) (3,0), (0, 3), (4, 2), & (7, 6)
c) (5,0), (0, 10), (4, 2) & (7, 6)
d) (0,18), (12, 0), (4, 2), (0, 0) and (7,6)

The Linear relationship between two variables in an inequality

a) ax + by ≤ c
b) ax by ≤ c
c) axy + by ≤ c
d) ax + bxy ≤ c

Cost of 5 mangoes and 2 apples can be at the most Rs 36. This can be represented by
a) 5x+2y>36
b) 5x+2y≥36
c) 5x+2y≤36
d) 5x+2y<36

Notes

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