Home » If x is negative, what is the range of values of x within which (frac{x…

If x is negative, what is the range of values of x within which (frac{x…

If x is negative, what is the range of values of x within which (frac{x + 1}{3}) > (frac{1}{X + 3})
  • A.
    3
  • B.
    -4
  • C.
    -2
  • D.
    -3
Correct Answer: Option B
Explanation

(frac{x + 1}{3}) > (frac{1}{X + 3}) = (frac{x + 1}{3}) > (frac{x + 3}{X + 3})
= (x + 1)(x + 3)2 > 3(x + 3) = (x + 1)[x2 + 6x + 9] > 3(x + 3)
x3 + 7x2 + 15x + 9 > 3x + 9 = x3 + 7x2 + 12x > 0
= x(x + 3)9x + 4) > 0
Case 1 (+, +, +) = x > 0 , x + 3 > 0, x + 4 > 0
= x > -4 (solution only)
Case 2 (+, -, -) = x > 0, x + 4

= x > 0, x

Case 3 (-, +, -) = x -3, x

Case 4 (-, -, +) = x 0
= x -4 = x

combining the solutions -4