Solve and graph inequalities on a number line with this engaging math worksheet.

It looks like you've uploaded a worksheet titled "SEE SPOT... Solve & Graph Inequalities", which is a fun, dog-themed math activity designed to help students practice solving and graphing linear inequalities. The worksheet includes 12 inequality problems labeled A through L, and for each problem, there’s a number line with a red arrow indicating the solution set.

Your task is to:
1. Solve each inequality.
2. Match the solution to the correct number line graph.
3. Write the letter of the inequality in the box next to its corresponding solution (graph).

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🔍 Let's go step by step and solve each inequality:

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#### A. 9 > 3 - 4x
Solve:
- Subtract 3 from both sides:
$ 9 - 3 > -4x $ → $ 6 > -4x $
- Divide by -4 (remember: flip inequality when dividing by negative):
$ \frac{6}{-4} < x $ → $ -\frac{3}{2} < x $ or $ x > -1.5 $

✔ Solution: $ x > -1.5 $ → open circle at -1.5, arrow to the right.

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#### B. 12 – 13 ≤ 8(–4 + 3x)
Simplify left side:
$ -1 ≤ 8(-4 + 3x) $ → $ -1 ≤ -32 + 24x $
Add 32:
$ 31 ≤ 24x $
Divide by 24:
$ x ≥ \frac{31}{24} $ ≈ $ x ≥ 1.29 $

✔ Solution: $ x ≥ 1.29 $ → closed circle at ~1.3, arrow to the right.

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#### C. –20 > 5(1 – 7x)
Distribute:
$ -20 > 5 - 35x $
Subtract 5:
$ -25 > -35x $
Divide by -35 (flip inequality):
$ \frac{-25}{-35} < x $ → $ \frac{5}{7} < x $ → $ x > \frac{5}{7} $ ≈ $ x > 0.714 $

✔ Solution: $ x > 0.714 $ → open circle at ~0.7, arrow to the right.

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#### D. –3x – 7 ≥ 2 – 4x
Move variables to one side:
Add 4x to both sides:
$ x - 7 ≥ 2 $
Add 7:
$ x ≥ 9 $

✔ Solution: $ x ≥ 9 $ → closed circle at 9, arrow to the right.

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#### E. –8x – 3 ≤ –83
Add 3:
$ -8x ≤ -80 $
Divide by -8 (flip inequality):
$ x ≥ 10 $

✔ Solution: $ x ≥ 10 $ → closed circle at 10, arrow to the right.

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#### F. 9 + 5x < 59
Subtract 9:
$ 5x < 50 $
Divide by 5:
$ x < 10 $

✔ Solution: $ x < 10 $ → open circle at 10, arrow to the left.

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#### G. 13 + 9x ≤ 1 + 10x
Subtract 9x:
$ 13 ≤ 1 + x $
Subtract 1:
$ 12 ≤ x $ → $ x ≥ 12 $

✔ Solution: $ x ≥ 12 $ → closed circle at 12, arrow to the right.

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#### H. –5 + 3x ≥ 13
Add 5:
$ 3x ≥ 18 $
Divide by 3:
$ x ≥ 6 $

✔ Solution: $ x ≥ 6 $ → closed circle at 6, arrow to the right.

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#### I. 4x + 7 ≤ –5 – 2x
Add 2x:
$ 6x + 7 ≤ -5 $
Subtract 7:
$ 6x ≤ -12 $
Divide by 6:
$ x ≤ -2 $

✔ Solution: $ x ≤ -2 $ → closed circle at -2, arrow to the left.

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#### J. 3x – 4 > 2x – 3x
Simplify right side: $ 2x - 3x = -x $
So: $ 3x - 4 > -x $
Add x: $ 4x - 4 > 0 $
Add 4: $ 4x > 4 $
Divide by 4: $ x > 1 $

✔ Solution: $ x > 1 $ → open circle at 1, arrow to the right.

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#### K. –4 + 4 ≤ 5x + 12
Simplify left: $ -8 ≤ 5x + 12 $
Subtract 12: $ -20 ≤ 5x $
Divide by 5: $ -4 ≤ x $ → $ x ≥ -4 $

✔ Solution: $ x ≥ -4 $ → closed circle at -4, arrow to the right.

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#### L. –10(–13 + x) ≥ –40
Distribute: $ 130 - 10x ≥ -40 $
Subtract 130: $ -10x ≥ -170 $
Divide by -10 (flip inequality): $ x ≤ 17 $

✔ Solution: $ x ≤ 17 $ → closed circle at 17, arrow to the left.

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✔ Now match solutions to graphs:

Let’s look at the graphs (numbered 1 to 12):

| Graph # | Description |
|--------|-------------|
| 1 | Open circle at -1.5, arrow right → $ x > -1.5 $ → A |
| 2 | Closed circle at 1.3, arrow right → $ x ≥ 1.29 $ → B |
| 3 | Open circle at 0.7, arrow right → $ x > 0.714 $ → C |
| 4 | Closed circle at 9, arrow right → $ x ≥ 9 $ → D |
| 5 | Closed circle at 10, arrow right → $ x ≥ 10 $ → E |
| 6 | Open circle at 10, arrow left → $ x < 10 $ → F |
| 7 | Closed circle at 12, arrow right → $ x ≥ 12 $ → G |
| 8 | Closed circle at 6, arrow right → $ x ≥ 6 $ → H |
| 9 | Closed circle at -2, arrow left → $ x ≤ -2 $ → I |
| 10 | Open circle at 1, arrow right → $ x > 1 $ → J |
| 11 | Closed circle at -4, arrow right → $ x ≥ -4 $ → K |
| 12 | Closed circle at 17, arrow left → $ x ≤ 17 $ → L |

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📌 Final Matching:

Now write the letter of the inequality in the box next to the graph:

| Graph | Letter |
|-------|--------|
| 1 | A |
| 2 | B |
| 3 | C |
| 4 | D |
| 5 | E |
| 6 | F |
| 7 | G |
| 8 | H |
| 9 | I |
| 10 | J |
| 11 | K |
| 12 | L |

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✔ Summary Answer:

You should fill in the boxes under each graph with the following letters:

- Graph 1: A
- Graph 2: B
- Graph 3: C
- Graph 4: D
- Graph 5: E
- Graph 6: F
- Graph 7: G
- Graph 8: H
- Graph 9: I
- Graph 10: J
- Graph 11: K
- Graph 12: L

This completes the "See Spot..." activity!

Let me know if you'd like this formatted as a printable answer key! 🐶🐶