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Question

If 5x+(23)2x13x, then the solution set for x is

A
[2,]
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B
{2}
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C
(,2]
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D
[0,2]
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Solution

The correct option is C (,2]
(513)x+(1213)x1
cosxα+sinxα1, where cosα=513
Equality holds for x=2.
If x<2, both cosα and sinα increase (being positive fractions).
So, cosxα+sinxα1 if x2.
Thus, x2.

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