Question:
Solve the given inequality for real $x: 2(2 x+3)-10<6(x-2)$
Solution:
$2(2 x+3)-10<6(x-2)$
$\Rightarrow 4 x+6-10<6 x-12$
$\Rightarrow 4 x-4<6 x-12$
$\Rightarrow-4+12<6 x-4 x$
$\Rightarrow 8<2 x$
$\Rightarrow 4 Thus, all real numbers $x$, which are greater than or equal to 4, are the solutions of the given inequality. Hence, the solution set of the given inequality is $(4, \infty)$.