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Question

If y is an integer number then which of the following is true for 2y3<y+14y+7?

A
Solution set = {-2, -1, 0, 1, 2, 3}
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B
Solution set = {-1, 0, 1, 2, 3, 4}
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C
Solution set = {-2, -1, 0, 1, 2, 3, 4}
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D
Solution set = {-2, -1, 0, 1, 2, 3, 4, 5}
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Solution

The correct option is A Solution set = {-2, -1, 0, 1, 2, 3}
Given: 2y3<y+14y+7

2y3<y+1 and y+14y+7

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequation.

2yy<3+1 and 174yy


y<4 and 63y

y<4 and y2

2y<4

Therefore, the solution set = {-2, -1, 0, 1, 2, 3}.

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