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PolarNik [594]
3 years ago
9

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

Mathematics
2 answers:
mars1129 [50]3 years ago
6 0

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.

Eduardwww [97]3 years ago
5 0
First solve the 2 inequalities for x:-

x > 0  or x <= -5


The last choice is the correct one.
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