Question

Solve the compound d Inequalities, graph the solutions and write the solutions in interval notation. I have (-infinity,-2) U (2, infinity)

Answer 1

Given:

`3x-1>5\text{ or }(x)/(2)-4<-5`

To find the solutions for this compound inequality, we will first need to solve for x.

`3x-1>5`
`3x>5+1`
`3x>6`
`x>2`

Since x > 2, this would give us an interval notation of ( 2, ∞ )

`(x)/(2)-4<-5`
`(x)/(2)<-5+4`
`(x)/(2)<-1`
`x<-1(2)`
`x<-2`

Now, since x < -2, this will give us an interval notation of ( -∞, -2 )

Since we see the word OR in our compound inequality, this would mean that the solution for this is ( -∞, -2 ) ∪ ( 2, ∞ )