Question

solve the compound inequality. graph the solution set and write it in interval notation
x < 5 or x < 8

choose the correct graph below.
a.
<----|----|----|----|----|----|----|----|----|----|----|----|----|---->
-4 -2 0 2 4 6 8 10 12 14
(blue line starts at 5, arrow right)
b.
<----|----|----|----|----|----|----|----|----|----|----|----|----|---->
-4 -2 0 2 4 6 8 10 12 14
(blue line ends at 8, arrow left)
c.
<----|----|----|----|----|----|----|----|----|----|----|----|----|---->
-4 -2 0 2 4 6 8 10 12 14
) (blue line ends at 8, arrow left)
d.
<----|----|----|----|----|----|----|----|----|----|----|----|----|---->
-4 -2 0 2 4 6 8 10 12 14
(blue line with no endpoints, arrow left)

Explanation:

Step1: Analyze the compound inequality

The compound inequality is \( x < 5 \) or \( x < 8 \). The "or" means we take the union of the solution sets of each inequality. The solution set of \( x < 5 \) is all real numbers less than 5, and the solution set of \( x < 8 \) is all real numbers less than 8. The union of these two sets is all real numbers less than 8 (since all numbers less than 5 are already less than 8).

Step2: Match with the graphs

• Option A: Starts at 5 (closed circle) and goes right, which is \( x\geq5 \), not our solution.
• Option B: Ends at 8 (closed circle) and goes left, which is \( x\leq8 \), not our solution (we need open at 8 since \( x < 8 \)).
• Option C: Has an open circle at 8 and goes left, which represents \( x < 8 \), matching our solution.
• Option D: No blue line, not our solution.

Answer:

C