Question

Solve the following inequality. $\frac{3x+6}{2x-12}\le 0$

• A. $-2\le x<6$
• B. $-2\le x<-6$
• C. $2\le x<6$
• D. None of these

Answer 1

Answer: (A)

$-2\le x<6$

The given inequality is,

$\frac{3x+6}{2x-12}\le 0$

There are following two possibilies-

Case (i) $3x+6\ge 0$ and $2x-12<0$

$\therefore 3x\ge -6$ and $2x<12$

$\therefore x\ge -2$ and $x<6$

Thus, we can write domain of the solution as, $-2\le x<6$

Case (ii) $3x+6\le 0$ and $2x-12>0$

$\therefore 3x\le -6$ and $2x>12$

$\therefore x\le -2$ and $x>6$

Satisfying these two conditions simultaneously is not possible. Thus solution of this inequality is $-2\le x<6$

Thus, Answer is option (A)