Solve the inequality (x-2)(x+2) > (x-2)(x+3)?

Feb 14, 2018

$x < 2$

Explanation:

$\left(x - 2\right) \left(x + 2\right) > \left(x - 2\right) \left(x + 3\right)$

means $\left(x - 2\right) \left(x + 2\right) - \left(x - 2\right) \left(x + 3\right) > 0$

or $\left(x - 2\right) \left(x + 2 - \left(x + 3\right)\right) > 0$

or $\left(x - 2\right) \left(x + 2 - x - 3\right) > 0$

or $\left(x - 2\right) \cdot \left(- 1\right) > 0$

or $- x + 2 > 0$

or $x < 2$