Respuesta :
first solve the 2 inequalities for x:-
x > 0 or x <= -5
The last choice is the correct one.
x > 0 or x <= -5
The last choice is the correct one.
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 :
[tex]2(x+3)>6~~\textup{or}~~2x+3\leq-7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the correct solution, we need to solve both the inequalities in (i) separately.
The solution of (i) is as follows :
[tex]2(x+3)>6\\\\\Rightarrow x+3>\dfrac{6}{2}\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0[/tex]
and
[tex]2x+3\leq -7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq-10\\\\\Rightarrow x\leq-\dfrac{10}{2}\\\\\Rightarrow x\leq -5.[/tex]
That is, the solution is given by
[tex]x\epsilon (-\infty,-5]~or~(0,\infty).[/tex]
Thus, (D) is the correct option.
