Question

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

2(x+3)>6  or  2x+3≤−7

A (−∞, −5] or (0, ∞)
B (−∞, 0) or [5, ∞)
C (−∞, −2] or (0, ∞)
D (−∞, −5] or (2, ∞)

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 .