Graph the compound inquality on the number line.

x< 3 or x > 6

To graph the compound inequality "x < 3 or x > 6" on a number line, follow these steps:

1. Draw a straight line with an arrow on both ends to represent the number line.

---->-----|------|-----|------|-----|------|----->
-∞ 3 6 ∞

Label key points on the number line using the numbers mentioned in the inequality. Here, the key points are -∞ (negative infinity), 3, 6, and ∞ (infinity).

2. Plot an open circle at the number 3 because the inequality is "x < 3" (not including 3).

---->-----|-----●|-----|------|-----|------|----->
-∞ 3 6 ∞

3. Draw an arrow to the left of the open circle towards negative infinity to represent the part of the number line where x is less than 3.

---->-----|----->|-----|------|-----|------|----->
-∞ 3 6 ∞

4. Plot an open circle at the number 6 because the inequality is "x > 6" (not including 6).

---->-----|----->|-----●-----|-----|------|----->
-∞ 3 6 ∞

5. Draw an arrow to the right of the open circle towards infinity to represent the part of the number line where x is greater than 6.

---->-----|----->|-----●-----►-----|------|----->
-∞ 3 6 ∞

6. The graph is complete. The shaded sections indicate all the possible values of x that satisfy the compound inequality "x < 3 or x > 6."