Number of integral values of x satisfying the inequality x 2 + 6 x - 7 x + 2 x + 3 < 0 is

Step-by-step solution

We have x 2 + 6 x - 7 x + 2 x + 3 < 0 . Clearly by modulus function property x + 2 ≥ 0   &   x + 3 ≥ 0 and x ≠ - 2 ,   - 3 . Now, x 2 + 6 x - 7 < 0 . ⇒ x 2 + 7 x - x - 7 < 0 ⇒ x + 7 x - 1 < 0 Using Sign Scheme for this expression, ⇒ x ∈ - 7 , 1 - - 3 , - 2 So, integers are - 6 , - 5 , - 4 , - 1 , 0 . So, total number of integral values of x = 5 .