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Find the largest integer value of x such that the following inequality holds:

(10 C x-1) <2*(10 C x)

In this question if solved line by line i am getting x<6.

but clearly if you put x=7, it satisfies the inequality and 7 becomes the largest integer.

Is there a procedure to get answer 7 step by step??
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I am getting 7 as answer, check if you are making any calculation mistake.

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