Question

Solve: x^2 - | x | - 12 < 0​

Answer 1

Solution!!

x² - | x | - 12 < 0

Separating the inequality into 2 possible cases.

x² - x - 12 < 0 , x ≥ 0

x² - (-x) - 12 < 0 , x < 0

Solving for x.

x² + 3x - 4x - 12 < 0 , x ≥ 0

x² + x - 12 < 0 , x < 0

x(x + 3) - 4(x + 3) < 0

x² + 4x - 3x - 12 < 0

(x + 3)(x - 4) < 0

x(x + 4) - 3(x + 4) < 0

x < -3 or x < 4

(x + 4)(x - 3) < 0

x < -3 or x < 4

x < -4 or x < 3

x ∈ (-3 , 4) , x ≥ 0

x ∈ (-4 , 3) , x < 0

Finding the intersection.

x ∈ (0 , 4) , x ≥ 0

x ∈ (-4 , 0) , x < 0

Finding the union.

x ∈ (-4 , 4)

Intersection of two sets contain only the elements that are in both the sets.

Union of two sets contains all the elements of one set or both the sets..