Range of values that represent Motion of the System...?

Question

Suppose that the total energy of the system is a constant, E = 2. Find the range or ranges of x-values that could represent a motion of the system. 

Updated 2 days ago:

How do you find EXACT values by just drawing the line and finding the points. Is there a way to calculate this or not?

Updated 2 days ago:

*** do I just make the equation of U(x) equal to 2 and then solve? 

Answer 1

The solution is that kinetic energy must exist whenever the potential energy is less than 2.  Both of the other answers are a part. 

Solve the equation for U(x) = 2 to give the crossing points then identify the regions where U <2

ie a) x<-1.8  b) -1.3<x<1  c) x>1.9

You can find the points accurately by finding the solutions of the equation.

Answer 2

Set U(x) = 2

2 = (equation)

Answer 3

Make a horizontal line on Y = 2, and wherever the line intersects are those range of values that could represent the motion of the system