Question

What is the solution to the compound inequality in interval notation? 2(x+3)>6 or 2x+3≤−7

Answer 1

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



hope this helps

Answer 2

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

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

`2(x+3)>6~or~2x+3\leq -7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

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

The inequality (i) can be solved as follows :

`2(x+3)>6\\\\\Rightarrow x+3>(6)/(2)\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0\\\\\Rightarrow x\epsilon (0,\infty)`

or

`2x+3\leq-7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq -10\\\\\Rightarrow x\leq -(10)/(2)\\\\\Rightarrow x\leq-5\\\\\Rightarrow x\epsilon(-\infty,-5].`

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