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If $\dfrac{(2y+1)}{(y+2)} < 1,$ then which of the following alternatives gives the CORRECT range of $y$ ?

  1. $- 2 < y < 2$
  2. $- 2 < y < 1$
  3. $- 3 < y < 1$
  4. $- 4 < y < 1$
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-2 gives not determined so y cannot be -3 , -4 as they will include -2 in there range, now from a and b .

putting y=1 gives 1. as stated it should be less than 1 so B is the correct answer
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while solving inequalities, the direction of inequality

  • doesn’t change
    • when a number is added or subtracted on both sides
    • when a positive number is multiplied or divided on both sides
  • changes
    • when a negative number is multiplied or divided on both sides

$\therefore$ The answer is option $\LARGE B$

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