Question

Solve the inequality $-3\le 3-2x<9,x\in R.$

Answer 1

We have $-3\le 3-2x<9$

$\Rightarrow$ $-3\le 3-2xand3-2x<9$

Now, $-3\le 3-2x$

$\Rightarrow$ $2x\le 3+3\Rightarrow 2x\le 6$

$\Rightarrow$ $x\le 3...\left(i\right)$

Again $3-2x<9$

$\Rightarrow$ $-2x<9-3\Rightarrow -2x<6$

$\Rightarrow$ $2x>-6\Rightarrow x>-3$ $[if-a<b,thena>-b]...\left(ii\right)$

From Eqs. (i) and (ii), we get

$x>-3andx\le 3$

$\therefore$ $-3<x\le 3$

Hence, solution set = $\{x\in R,-3<x\le 3\}.$