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:

$3x-1>5\text{ or }\frac{x}{2}-4<-5$

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, ∞ )

$\frac{x}{2}-4<-5$$\frac{x}{2}<-5+4$$\frac{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, ∞ )