Question

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

Answer 1

Answer:  The correct option is

(D) (−∞, −5] or (0, ∞).

Step-by-step explanation:  We are given to select the solution to the following inequality in interval notation :

$2(x+3)>6~~\textup{or}~~2x+3\leq-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To find the correct solution, we need to solve both the inequalities in (i) separately.

The solution of (i) is as follows :

$2(x+3)>6\\\\\Rightarrow x+3>\dfrac{6}{2}\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0$

and

$2x+3\leq -7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq-10\\\\\Rightarrow x\leq-\dfrac{10}{2}\\\\\Rightarrow x\leq -5.$

That is, the solution is given by

$x\epsilon (-\infty,-5]~or~(0,\infty).$

Thus, (D) is the correct option.

Answer 2

First solve the 2 inequalities for x:-

x > 0  or x <= -5


The last choice is the correct one.