Describe the real numbers x for which (−x) < (x^2 − 12 )< (4x).
-x < x²-12 < 4x
=> -x < x²-12 and x²-12 < 4x
=> x² +x - 12 > 0 and x² - 4x - 12 < 0
=> (x+4)(x - 3) > 0 and (x - 6)(x+2)<0
=> x ∈(−∞,−4)⋃(3,∞)\in(-∞,-4)\bigcup(3,∞)∈(−∞,−4)⋃(3,∞) and x∈(−2,6)\in(-2,6)∈(−2,6)
So x∈(3,6)x\in(3,6)x∈(3,6)
So x is a real number such that 3< x < 6
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