Question

Describe the real numbers x for which (−x) < (x^2 − 12 )< (4x).

Answer 1

-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 $\in(-∞,-4)\bigcup(3,∞)$ and x$\in(-2,6)$

So $x\in(3,6)$

So x is a real number such that 3< x < 6