Question

answer attempt 2 out of 2
inequality notation: x ≤ 6 or x ≥ 9
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Explanation:

To graph the inequality \( x \leq 6 \) or \( x \geq 9 \) on the number line:

Step 1: Graph \( x \leq 6 \)

• Locate 6 on the number line.
• Since \( x \leq 6 \) includes 6, we use a closed (filled) circle at 6.
• Draw an arrow to the left from 6 to represent all numbers less than or equal to 6.

Step 2: Graph \( x \geq 9 \)

• Locate 9 on the number line.
• Since \( x \geq 9 \) includes 9, we use a closed (filled) circle at 9.
• Draw an arrow to the right from 9 to represent all numbers greater than or equal to 9.

Final Graph Description

• At 6: Closed circle, arrow left.
• At 9: Closed circle, arrow right.
• The regions are separated (no overlap between \( x \leq 6 \) and \( x \geq 9 \) except if 6 and 9 were equal, which they aren’t, so the "or" means the solution is the union of these two intervals).

(Visually, on the given number line with marks at -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12: place a closed dot at 6 and draw left, closed dot at 9 and draw right.)

If you needed the inequality notation (already given as \( x \leq 6 \) or \( x \geq 9 \)) and the number line graph as described, that’s the solution.

Answer:

To graph the inequality \( x \leq 6 \) or \( x \geq 9 \) on the number line:

Step 1: Graph \( x \leq 6 \)

• Locate 6 on the number line.
• Since \( x \leq 6 \) includes 6, we use a closed (filled) circle at 6.
• Draw an arrow to the left from 6 to represent all numbers less than or equal to 6.

Step 2: Graph \( x \geq 9 \)

• Locate 9 on the number line.
• Since \( x \geq 9 \) includes 9, we use a closed (filled) circle at 9.
• Draw an arrow to the right from 9 to represent all numbers greater than or equal to 9.

Final Graph Description

• At 6: Closed circle, arrow left.
• At 9: Closed circle, arrow right.
• The regions are separated (no overlap between \( x \leq 6 \) and \( x \geq 9 \) except if 6 and 9 were equal, which they aren’t, so the "or" means the solution is the union of these two intervals).

(Visually, on the given number line with marks at -12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12: place a closed dot at 6 and draw left, closed dot at 9 and draw right.)

If you needed the inequality notation (already given as \( x \leq 6 \) or \( x \geq 9 \)) and the number line graph as described, that’s the solution.