Solve the inequality and graph the solution.

Question

2<
q
4
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( 2 < q < 4 \):

1. Identify the endpoints: The endpoints are \( 2 \) and \( 4 \).
2. Determine whether to make endpoints open or closed:
   • Since the inequality is strictly less than and does not include \( 2 \) or \( 4 \), both endpoints should be open.
3. Graph the solution:
   • Draw a number line.
   • Place an open circle at \( 2 \) (indicating \( 2 \) is not included in the solution).
   • Place an open circle at \( 4 \) (indicating \( 4 \) is not included in the solution).
   • Shade the region between \( 2 \) and \( 4 \).

Solution summary:

The solution in interval notation is \( (2, 4) \).

Graph representation:

  ------------------------------------- 
2       3       4
  (-----------------)

Here, the parentheses indicate open endpoints, and the shaded region represents all \( q \) values that satisfy the inequality \( 2 < q < 4 \).