Solve the inequality 2 (2x + 3) – 10 < 6 (x – 2) for real x. - Vidyadip

Question

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

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Answer

Here 2(2x + 3) - 10 < 6(x - 2)
$ \Rightarrow 4x + 6 - 10 < 6x - 12$
$ \Rightarrow 4x - 4 < 6x - 12$
$ \Rightarrow 4x - 6x < - 12 + 4$
$ \Rightarrow - 2x < - 8$
Dividing both sides by -2, we have
$\frac{{ - 2x}}{{ - 2}} > \frac{{ - 8}}{{ - 2}}$
$ \Rightarrow x > 4$
Thus the solution set is $(4,\infty )$

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