Question
Question: The set of all real values of x satisfying the inequality \|x<sup>2</sup> + x – 6\| \< 6 is :...
The set of all real values of x satisfying the inequality
|x2 + x – 6| < 6 is :
A
(– 4, 3)
B
(–3, 2)
C
(– 4, –3)∪(2, 3)
D
(– 4, – 1)∪(0, 3)
Answer
(– 4, – 1)∪(0, 3)
Explanation
Solution
– 6 < x2 + x – 6 < 6
x2 + x > 0 , x2 + x – 12 < 0
x(x + 1) > 0, (x + 4)(x – 3) < 0
x∈ (– ∞, –1) ∪ (0, ∞), x∈(– 4, 3)
common
x∈(– 4, –1) ∪ (0, 3)