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# Write the set of values of x satisfying the inequations 5x + 2 < 3x + 8 and .

Part I : 5x + 2 < 3x + 8

2x < 6

x < 3

Part II :    Case I : -3x + 6 < 0 and x – 1 > 0

x > 2 and x > 1

By taking intersection x (2, ∞)

Case II : -3x + 6 > 0 and x – 1 < 0

x < 2 and x < 1

By takin intersection x (-∞, 1)

Taking union of case I and case II, x (-∞, 1) (2, ∞)

We have to take intersection of part I and part II, we have

final answer i.e., x (-∞, 1) (2, 3)

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