Solve algebra equations to color a fun mandala design in this educational worksheet.

This is a "Color by Number" activity that involves solving algebraic equations to determine which color to use for each section of the image. Here's how to solve the problem step by step:

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Step 1: Understand the Task

- The image contains a circular design divided into sections, each labeled with an algebraic equation.
- Solve each equation to find the value of \( x \).
- Match the value of \( x \) to the corresponding color code provided at the top of the page.

Step 2: Color Code Reference

The color codes are as follows:
- \( 3 = \text{blue} \)
- \( 4 = \text{pink} \)
- \( 5 = \text{purple} \)
- \( 6 = \text{red} \)
- \( 7 = \text{green} \)
- \( 8 = \text{orange} \)
- \( 9 = \text{yellow} \)

Step 3: Solve Each Equation

We will solve each equation one by one and determine the value of \( x \). Then, we'll match the value to the color code.

#### Equation 1: \( -2x + 59 = 41 \)
\[
-2x + 59 = 41
\]
Subtract 59 from both sides:
\[
-2x = 41 - 59
\]
\[
-2x = -18
\]
Divide by -2:
\[
x = \frac{-18}{-2} = 9
\]
Color: Yellow

#### Equation 2: \( 60 + 2x = 74 \)
\[
60 + 2x = 74
\]
Subtract 60 from both sides:
\[
2x = 74 - 60
\]
\[
2x = 14
\]
Divide by 2:
\[
x = \frac{14}{2} = 7
\]
Color: Green

#### Equation 3: \( 88 - 5x = 53 \)
\[
88 - 5x = 53
\]
Subtract 88 from both sides:
\[
-5x = 53 - 88
\]
\[
-5x = -35
\]
Divide by -5:
\[
x = \frac{-35}{-5} = 7
\]
Color: Green

#### Equation 4: \( 103 - 8x = 79 \)
\[
103 - 8x = 79
\]
Subtract 103 from both sides:
\[
-8x = 79 - 103
\]
\[
-8x = -24
\]
Divide by -8:
\[
x = \frac{-24}{-8} = 3
\]
Color: Blue

#### Equation 5: \( 1x + 64 = 67 \)
\[
1x + 64 = 67
\]
Subtract 64 from both sides:
\[
x = 67 - 64
\]
\[
x = 3
\]
Color: Blue

#### Equation 6: \( 65 + -4x = 29 \)
\[
65 - 4x = 29
\]
Subtract 65 from both sides:
\[
-4x = 29 - 65
\]
\[
-4x = -36
\]
Divide by -4:
\[
x = \frac{-36}{-4} = 9
\]
Color: Yellow

#### Equation 7: \( 23 + 4x = 55 \)
\[
23 + 4x = 55
\]
Subtract 23 from both sides:
\[
4x = 55 - 23
\]
\[
4x = 32
\]
Divide by 4:
\[
x = \frac{32}{4} = 8
\]
Color: Orange

#### Equation 8: \( -4x + 49 = 55 \)
\[
-4x + 49 = 55
\]
Subtract 49 from both sides:
\[
-4x = 55 - 49
\]
\[
-4x = 6
\]
Divide by -4:
\[
x = \frac{6}{-4} = -1.5
\]
Since this value does not match any of the given color codes, it might be an error or an outlier. For now, we'll note it as "No Color."

#### Equation 9: \( 129 + -13x = 38 \)
\[
129 - 13x = 38
\]
Subtract 129 from both sides:
\[
-13x = 38 - 129
\]
\[
-13x = -91
\]
Divide by -13:
\[
x = \frac{-91}{-13} = 7
\]
Color: Green

#### Equation 10: \( 31 + 4x = 79 \)
\[
31 + 4x = 79
\]
Subtract 31 from both sides:
\[
4x = 79 - 31
\]
\[
4x = 48
\]
Divide by 4:
\[
x = \frac{48}{4} = 12
\]
Since this value does not match any of the given color codes, it might be an error or an outlier. For now, we'll note it as "No Color."

#### Equation 11: \( 110 - 8x = 70 \)
\[
110 - 8x = 70
\]
Subtract 110 from both sides:
\[
-8x = 70 - 110
\]
\[
-8x = -40
\]
Divide by -8:
\[
x = \frac{-40}{-8} = 5
\]
Color: Purple

#### Equation 12: \( 71 - 4x = 39 \)
\[
71 - 4x = 39
\]
Subtract 71 from both sides:
\[
-4x = 39 - 71
\]
\[
-4x = -32
\]
Divide by -4:
\[
x = \frac{-32}{-4} = 8
\]
Color: Orange

#### Equation 13: \( 18 + 2x = 12 \)
\[
18 + 2x = 12
\]
Subtract 18 from both sides:
\[
2x = 12 - 18
\]
\[
2x = -6
\]
Divide by 2:
\[
x = \frac{-6}{2} = -3
\]
Since this value does not match any of the given color codes, it might be an error or an outlier. For now, we'll note it as "No Color."

#### Equation 14: \( 71 + 1x = 74 \)
\[
71 + x = 74
\]
Subtract 71 from both sides:
\[
x = 74 - 71
\]
\[
x = 3
\]
Color: Blue

#### Equation 15: \( 6 + 3x = 44 \)
\[
6 + 3x = 44
\]
Subtract 6 from both sides:
\[
3x = 44 - 6
\]
\[
3x = 38
\]
Divide by 3:
\[
x = \frac{38}{3} \approx 12.67
\]
Since this value does not match any of the given color codes, it might be an error or an outlier. For now, we'll note it as "No Color."

#### Equation 16: \( 29 + 5x = 23 \)
\[
29 + 5x = 23
\]
Subtract 29 from both sides:
\[
5x = 23 - 29
\]
\[
5x = -6
\]
Divide by 5:
\[
x = \frac{-6}{5} = -1.2
\]
Since this value does not match any of the given color codes, it might be an error or an outlier. For now, we'll note it as "No Color."

#### Equation 17: \( 5 + 3x = 23 \)
\[
5 + 3x = 23
\]
Subtract 5 from both sides:
\[
3x = 23 - 5
\]
\[
3x = 18
\]
Divide by 3:
\[
x = \frac{18}{3} = 6
\]
Color: Red

#### Equation 18: \( -1x + 21 = 18 \)
\[
-1x + 21 = 18
\]
Subtract 21 from both sides:
\[
-1x = 18 - 21
\]
\[
-1x = -3
\]
Divide by -1:
\[
x = \frac{-3}{-1} = 3
\]
Color: Blue

#### Equation 19: \( 32 + 4x = 60 \)
\[
32 + 4x = 60
\]
Subtract 32 from both sides:
\[
4x = 60 - 32
\]
\[
4x = 28
\]
Divide by 4:
\[
x = \frac{28}{4} = 7
\]
Color: Green

#### Equation 20: \( 75 + 2x = 81 \)
\[
75 + 2x = 81
\]
Subtract 75 from both sides:
\[
2x = 81 - 75
\]
\[
2x = 6
\]
Divide by 2:
\[
x = \frac{6}{2} = 3
\]
Color: Blue

#### Equation 21: \( 120 + -7x = 65 \)
\[
120 - 7x = 65
\]
Subtract 120 from both sides:
\[
-7x = 65 - 120
\]
\[
-7x = -55
\]
Divide by -7:
\[
x = \frac{-55}{-7} \approx 7.86
\]
Since this value does not match any of the given color codes, it might be an error or an outlier. For now, we'll note it as "No Color."

#### Equation 22: \( 48 + 1x = 56 \)
\[
48 + x = 56
\]
Subtract 48 from both sides:
\[
x = 56 - 48
\]
\[
x = 8
\]
Color: Orange

#### Equation 23: \( -9 + 4x = 15 \)
\[
-9 + 4x = 15
\]
Add 9 to both sides:
\[
4x = 15 + 9
\]
\[
4x = 24
\]
Divide by 4:
\[
x = \frac{24}{4} = 6
\]
Color: Red

#### Equation 24: \( 39 + 3x = 54 \)
\[
39 + 3x = 54
\]
Subtract 39 from both sides:
\[
3x = 54 - 39
\]
\[
3x = 15
\]
Divide by 3:
\[
x = \frac{15}{3} = 5
\]
Color: Purple

#### Equation 25: \( 5x - 12 = 28 \)
\[
5x - 12 = 28
\]
Add 12 to both sides:
\[
5x = 28 + 12
\]
\[
5x = 40
\]
Divide by 5:
\[
x = \frac{40}{5} = 8
\]
Color: Orange

#### Equation 26: \( 71 + 3x = 86 \)
\[
71 + 3x = 86
\]
Subtract 71 from both sides:
\[
3x = 86 - 71
\]
\[
3x = 15
\]
Divide by 3:
\[
x = \frac{15}{3} = 5
\]
Color: Purple

#### Equation 27: \( 122 + -12x = 38 \)
\[
122 - 12x = 38
\]
Subtract 122 from both sides:
\[
-12x = 38 - 122
\]
\[
-12x = -84
\]
Divide by -12:
\[
x = \frac{-84}{-12} = 7
\]
Color: Green

#### Equation 28: \( 33 - 3x = 15 \)
\[
33 - 3x = 15
\]
Subtract 33 from both sides:
\[
-3x = 15 - 33
\]
\[
-3x = -18
\]
Divide by -3:
\[
x = \frac{-18}{-3} = 6
\]
Color: Red

#### Equation 29: \( 74 - 13x = 35 \)
\[
74 - 13x = 35
\]
Subtract 74 from both sides:
\[
-13x = 35 - 74
\]
\[
-13x = -39
\]
Divide by -13:
\[
x = \frac{-39}{-13} = 3
\]
Color: Blue

#### Equation 30: \( 2x + 18 = 26 \)
\[
2x + 18 = 26
\]
Subtract 18 from both sides:
\[
2x = 26 - 18
\]
\[
2x = 8
\]
Divide by 2:
\[
x = \frac{8}{2} = 4
\]
Color: Pink

#### Equation 31: \( 1x + 38 = 42 \)
\[
1x + 38 = 42
\]
Subtract 38 from both sides:
\[
x = 42 - 38
\]
\[
x = 4
\]
Color: Pink

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Step 4: Color the Image

Using the solutions above, color each section of the image according to the corresponding color code. Sections with values not matching the color codes can be left uncolored or marked as errors.

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Final Answer

\[
\boxed{\text{See the solved equations and color assignments above.}}
\]