Question

What is the solution to the compound inequality in interval notation?

Answer 1

The given compound inequality is

$2(x+3)>6 \ or \ 2x+3\leq -7$

First we solve the first inequality,

$2(x+3)>6 \\ x+3 >3 \\ x>0$

Now we solve the second inequality

$2x+3\leq -7 \\ 2x \leq -7-3 \\ 2x\leq -10 \\ x\leq -5$

So we have

$x > 0 \ or \ x\leq -5$

So the required solution is

$( - \infty,-5] \ or \ (0, \infty)$

Correct option is A .