First slide

Theory of equations

Question

The complete solution of the inequation $x^{2} - 4 x < 12$ is

Moderate

A

$x < - 2 or x > 6$
B

$- 6 < x < 2$
C

$2 < x < 6$
D

$- 2 < x < 6$

Solution

$x^{2} - 4 x < 12$
$\Rightarrow x^{2} - 4 x - 12 < 0 \Rightarrow x^{2} - 6 x + 2 x - 12 < 0$
$\Rightarrow (x - 6) (x + 2) < 0 \Rightarrow - 2 < x < 6 .$

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