Respuesta :

for 2(x+3)>6 x would = 0 and for 2x+3<-7  x would = -5



hope this helps

Answer:  The required solution in interval notation is [tex](0,\infty)U(-\infty,-5].[/tex]

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

[tex]2(x+3)>6~or~2x+3\leq -7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the solution to (i), we must solve both the parts separately.

The inequality (i) can be solved as follows :

[tex]2(x+3)>6\\\\\Rightarrow x+3>\dfrac{6}{2}\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0\\\\\Rightarrow x\epsilon (0,\infty)[/tex]

or

[tex]2x+3\leq-7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq -10\\\\\Rightarrow x\leq -\dfrac{10}{2}\\\\\Rightarrow x\leq-5\\\\\Rightarrow x\epsilon(-\infty,-5].[/tex]

Thus, the required solution in interval notation is [tex](0,\infty)U(-\infty,-5].[/tex]

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