Question

Solve the following system of inequations in $R.$

$x-2>0,3x<18$

Answer 1

Given system of inequations:

$x-2>0and3x<18$

Let us consider the first inequation.

$x-2>0$

Transposing $-2$ on R.H.S.

$\Rightarrow x>2$

$\therefore x\in (2,\infty )\dots \left(1\right)$

Now, let us consider the second inequation.

$3x<18$

Divide by 3 on both sides we get,

$\Rightarrow \frac{3x}{3}<\frac{18}{3}$

$\Rightarrow x<6$

$\therefore x\in (-\infty ,6)\dots \left(2\right)$


From (1) and (2) we get,

$x\in (2,\infty )\cap (-\infty ,6)$

$\therefore x\in (2,6)$



Thus, the solution set of the given system of inequations is $(2,6).$