Question

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

2(x+3)>6  or  2x+3≤−7

(−∞, 0) or [5, ∞)
(−∞, −5] or (2, ∞)
(−∞, −2] or (0, ∞)
(−∞, −5] or (0, ∞)

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>(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-(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.