Final Answer:
The number line graphs should be drawn as follows (described for each problem):
1) $ x > 12 $: Open circle at 12, arrow to the right.
2) $ x < 7 $: Open circle at 7, arrow to the left.
3) $ x \ge 9 $: Closed circle at 9, arrow to the right.
4) $ x \le 12 $: Closed circle at 12, arrow to the left.
5) $ x < 15 $: Open circle at 15, arrow to the left.
6) $ x \ge 11 $: Closed circle at 11, arrow to the right.
7) $ x > 4 $: Open circle at 4, arrow to the right.
8) $ x \le 6 $: Closed circle at 6, arrow to the left.
Since the task is to *solve* (i.e., correctly represent) the inequalities on the number lines, and no specific answer format (like multiple choice) is given, the correct solution is the set of proper graph markings above.
But if the expected output is just confirmation that the student should draw those graphs — and since the question is “Solve the problem accurately” — the final answer is the description of how each inequality is graphed.
However, per instruction:
"Provide only the final correct answer", and given this is a worksheet where students fill in the number lines, the *correct answer* is the set of graphical representations. Since we can’t draw here, the standard way to report it is by specifying the endpoint type and direction for each:
1) ○ at 12, →
2) ○ at 7, ←
3) ● at 9, →
4) ● at 12, ←
5) ○ at 15, ←
6) ● at 11, →
7) ○ at 4, →
8) ● at 6, ←
Using ○ for open circle (not included), ● for closed circle (included), → for right, ← for left.
Final Answer:
1) ○12→
2) ○7←
3) ●9→
4) ●12←
5) ○15←
6) ●11→
7) ○4→
8) ●6←
Parent Tip: Review the logic above to help your child master the concept of algebra inequalities number line worksheet.
