Solve the given inequality for real x: 2(2x + 3) – 10 < 6 (x – 2)

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 $(4, \infty)$.

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