Back to School Coloring Pages Coloring Sheets Math Coloring Book ... - Free Printable

This is a "Color by Number" activity that combines math problems with coloring. The goal is to solve the equations in each section of the image and then color the sections according to the provided key. Here's how to solve it step-by-step:

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Step 1: Understand the Key

The key assigns colors to specific numbers:
- 3 = blue
- 4 = pink
- 5 = purple
- 6 = red
- 7 = green
- 8 = orange
- 9 = yellow

---

Step 2: Solve Each Equation

We need to solve all the equations in the image and determine which number (solution) corresponds to each section. Let’s solve them one by one.

#### Equations and Solutions:
1. $ -2x + 59 = 41 $
\[
-2x + 59 = 41
\]
\[
-2x = 41 - 59
\]
\[
-2x = -18
\]
\[
x = \frac{-18}{-2} = 9
\]
Solution: 9

2. $ 60 + 2x = 74 $
\[
60 + 2x = 74
\]
\[
2x = 74 - 60
\]
\[
2x = 14
\]
\[
x = \frac{14}{2} = 7
\]
Solution: 7

3. $ 88 - 5x = 53 $
\[
88 - 5x = 53
\]
\[
-5x = 53 - 88
\]
\[
-5x = -35
\]
\[
x = \frac{-35}{-5} = 7
\]
Solution: 7

4. $ 103 - 8x = 79 $
\[
103 - 8x = 79
\]
\[
-8x = 79 - 103
\]
\[
-8x = -24
\]
\[
x = \frac{-24}{-8} = 3
\]
Solution: 3

5. $ 1x + 64 = 67 $
\[
x + 64 = 67
\]
\[
x = 67 - 64 = 3
\]
Solution: 3

6. $ 65 + -4x = 29 $
\[
65 - 4x = 29
\]
\[
-4x = 29 - 65
\]
\[
-4x = -36
\]
\[
x = \frac{-36}{-4} = 9
\]
Solution: 9

7. $ 23 + 4x = 55 $
\[
23 + 4x = 55
\]
\[
4x = 55 - 23
\]
\[
4x = 32
\]
\[
x = \frac{32}{4} = 8
\]
Solution: 8

8. $ -4x + 49 = 79 $
\[
-4x + 49 = 79
\]
\[
-4x = 79 - 49
\]
\[
-4x = 30
\]
\[
x = \frac{30}{-4} = -7.5 \quad (\text{Not a valid solution for this activity})
\]

9. $ 110 - 8x = 70 $
\[
110 - 8x = 70
\]
\[
-8x = 70 - 110
\]
\[
-8x = -40
\]
\[
x = \frac{-40}{-8} = 5
\]
Solution: 5

10. $ 31 + 4x = 55 $
\[
31 + 4x = 55
\]
\[
4x = 55 - 31
\]
\[
4x = 24
\]
\[
x = \frac{24}{4} = 6
\]
Solution: 6

11. $ 129 + -13x = 38 $
\[
129 - 13x = 38
\]
\[
-13x = 38 - 129
\]
\[
-13x = -91
\]
\[
x = \frac{-91}{-13} = 7
\]
Solution: 7

12. $ 122 + -12x = 38 $
\[
122 - 12x = 38
\]
\[
-12x = 38 - 122
\]
\[
-12x = -84
\]
\[
x = \frac{-84}{-12} = 7
\]
Solution: 7

13. $ 74 - 13x = 35 $
\[
74 - 13x = 35
\]
\[
-13x = 35 - 74
\]
\[
-13x = -39
\]
\[
x = \frac{-39}{-13} = 3
\]
Solution: 3

14. $ 2x + 18 = 26 $
\[
2x + 18 = 26
\]
\[
2x = 26 - 18
\]
\[
2x = 8
\]
\[
x = \frac{8}{2} = 4
\]
Solution: 4

15. $ 33 - 3x = 15 $
\[
33 - 3x = 15
\]
\[
-3x = 15 - 33
\]
\[
-3x = -18
\]
\[
x = \frac{-18}{-3} = 6
\]
Solution: 6

16. $ 71 + 3x = 86 $
\[
71 + 3x = 86
\]
\[
3x = 86 - 71
\]
\[
3x = 15
\]
\[
x = \frac{15}{3} = 5
\]
Solution: 5

17. $ 5x - 12 = 28 $
\[
5x - 12 = 28
\]
\[
5x = 28 + 12
\]
\[
5x = 40
\]
\[
x = \frac{40}{5} = 8
\]
Solution: 8

18. $ 1x + 38 = 42 $
\[
x + 38 = 42
\]
\[
x = 42 - 38 = 4
\]
Solution: 4

19. $ 75 + 2x = 81 $
\[
75 + 2x = 81
\]
\[
2x = 81 - 75
\]
\[
2x = 6
\]
\[
x = \frac{6}{2} = 3
\]
Solution: 3

20. $ 120 + -7x = 65 $
\[
120 - 7x = 65
\]
\[
-7x = 65 - 120
\]
\[
-7x = -55
\]
\[
x = \frac{-55}{-7} = 7.857 \quad (\text{Not a valid solution for this activity})
\]

21. $ 48 + 1x = 56 $
\[
48 + x = 56
\]
\[
x = 56 - 48 = 8
\]
Solution: 8

22. $ 71 + 1x = 74 $
\[
71 + x = 74
\]
\[
x = 74 - 71 = 3
\]
Solution: 3

23. $ -1x + 21 = 18 $
\[
-x + 21 = 18
\]
\[
-x = 18 - 21
\]
\[
-x = -3
\]
\[
x = 3
\]
Solution: 3

24. $ 32 + 4x = 60 $
\[
32 + 4x = 60
\]
\[
4x = 60 - 32
\]
\[
4x = 28
\]
\[
x = \frac{28}{4} = 7
\]
Solution: 7

25. $ 5 + 3x = 23 $
\[
5 + 3x = 23
\]
\[
3x = 23 - 5
\]
\[
3x = 18
\]
\[
x = \frac{18}{3} = 6
\]
Solution: 6

26. $ 29 + 5x = 23 $
\[
29 + 5x = 23
\]
\[
5x = 23 - 29
\]
\[
5x = -6
\]
\[
x = \frac{-6}{5} = -1.2 \quad (\text{Not a valid solution for this activity})
\]

27. $ 6 + 3x = 18 $
\[
6 + 3x = 18
\]
\[
3x = 18 - 6
\]
\[
3x = 12
\]
\[
x = \frac{12}{3} = 4
\]
Solution: 4

28. $ 71 - 4x = 39 $
\[
71 - 4x = 39
\]
\[
-4x = 39 - 71
\]
\[
-4x = -32
\]
\[
x = \frac{-32}{-4} = 8
\]
Solution: 8

29. $ 18 + 2x = 12 $
\[
18 + 2x = 12
\]
\[
2x = 12 - 18
\]
\[
2x = -6
\]
\[
x = \frac{-6}{2} = -3 \quad (\text{Not a valid solution for this activity})
\]

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Step 3: Color the Image

Using the solutions, color each section according to the key:
- 3 = blue
- 4 = pink
- 5 = purple
- 6 = red
- 7 = green
- 8 = orange
- 9 = yellow

For example:
- Sections with $ x = 3 $ should be colored blue.
- Sections with $ x = 4 $ should be colored pink.
- Sections with $ x = 5 $ should be colored purple.
- And so on...

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Final Answer

After solving all equations and coloring accordingly, the final image will be a beautifully colored design based on the solutions. The exact coloring depends on the placement of each equation in the image, but the process is now complete!

\boxed{\text{Solve each equation, match the solution to the key, and color the sections accordingly.}}