Solve algebra equations to color the mandala in this engaging math activity.

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

- Each section of the flower has an equation.
- Solve each equation to find the value of \( x \).
- Match the value of \( x \) to the corresponding number (3, 4, 5, 6, 7, 8, or 9) and use the provided color key to color the section.

Step 2: Solve Each Equation

We will solve each equation one by one and determine the value of \( x \).

#### Equation 1: \( 26 + -5x = 11 \)
\[
26 - 5x = 11
\]
Subtract 26 from both sides:
\[
-5x = 11 - 26
\]
\[
-5x = -15
\]
Divide by -5:
\[
x = 3
\]

#### Equation 2: \( 47 - 3x = 32 \)
\[
47 - 3x = 32
\]
Subtract 47 from both sides:
\[
-3x = 32 - 47
\]
\[
-3x = -15
\]
Divide by -3:
\[
x = 5
\]

#### Equation 3: \( 55 + 3x = 67 \)
\[
55 + 3x = 67
\]
Subtract 55 from both sides:
\[
3x = 67 - 55
\]
\[
3x = 12
\]
Divide by 3:
\[
x = 4
\]

#### Equation 4: \( 64 + -4x = 29 \)
\[
64 - 4x = 29
\]
Subtract 64 from both sides:
\[
-4x = 29 - 64
\]
\[
-4x = -35
\]
Divide by -4:
\[
x = 8.75 \quad (\text{Not in the given range})
\]

#### Equation 5: \( 73 + -3x = 55 \)
\[
73 - 3x = 55
\]
Subtract 73 from both sides:
\[
-3x = 55 - 73
\]
\[
-3x = -18
\]
Divide by -3:
\[
x = 6
\]

#### Equation 6: \( 6 + 3x = 15 \)
\[
6 + 3x = 15
\]
Subtract 6 from both sides:
\[
3x = 15 - 6
\]
\[
3x = 9
\]
Divide by 3:
\[
x = 3
\]

#### Equation 7: \( 157 + 11x = 69 \)
\[
157 + 11x = 69
\]
Subtract 157 from both sides:
\[
11x = 69 - 157
\]
\[
11x = -88
\]
Divide by 11:
\[
x = -8 \quad (\text{Not in the given range})
\]

#### Equation 8: \( 67 - 4x = 46 \)
\[
67 - 4x = 46
\]
Subtract 67 from both sides:
\[
-4x = 46 - 67
\]
\[
-4x = -21
\]
Divide by -4:
\[
x = 5.25 \quad (\text{Not in the given range})
\]

#### Equation 9: \( 102 - 12x = 66 \)
\[
102 - 12x = 66
\]
Subtract 102 from both sides:
\[
-12x = 66 - 102
\]
\[
-12x = -36
\]
Divide by -12:
\[
x = 3
\]

#### Equation 10: \( 44 - 2x = 30 \)
\[
44 - 2x = 30
\]
Subtract 44 from both sides:
\[
-2x = 30 - 44
\]
\[
-2x = -14
\]
Divide by -2:
\[
x = 7
\]

#### Equation 11: \( 85 - 2x = 67 \)
\[
85 - 2x = 67
\]
Subtract 85 from both sides:
\[
-2x = 67 - 85
\]
\[
-2x = -18
\]
Divide by -2:
\[
x = 9
\]

#### Equation 12: \( 103 - 4x = 71 \)
\[
103 - 4x = 71
\]
Subtract 103 from both sides:
\[
-4x = 71 - 103
\]
\[
-4x = -32
\]
Divide by -4:
\[
x = 8
\]

#### Equation 13: \( 34 + 5x = 64 \)
\[
34 + 5x = 64
\]
Subtract 34 from both sides:
\[
5x = 64 - 34
\]
\[
5x = 30
\]
Divide by 5:
\[
x = 6
\]

#### Equation 14: \( -4x + 7 = 43 \)
\[
-4x + 7 = 43
\]
Subtract 7 from both sides:
\[
-4x = 43 - 7
\]
\[
-4x = 36
\]
Divide by -4:
\[
x = -9 \quad (\text{Not in the given range})
\]

#### Equation 15: \( 76 + 2x = 86 \)
\[
76 + 2x = 86
\]
Subtract 76 from both sides:
\[
2x = 86 - 76
\]
\[
2x = 10
\]
Divide by 2:
\[
x = 5
\]

#### Equation 16: \( 109 - 4x = 73 \)
\[
109 - 4x = 73
\]
Subtract 109 from both sides:
\[
-4x = 73 - 109
\]
\[
-4x = -36
\]
Divide by -4:
\[
x = 9
\]

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Step 3: Match Values to Colors

Using the solved values of \( x \), match them to the color key:
- \( x = 3 \): Blue
- \( x = 4 \): Pink
- \( x = 5 \): Purple
- \( x = 6 \): Red
- \( x = 7 \): Green
- \( x = 8 \): Orange
- \( x = 9 \): Yellow

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Final Answer

Color each section based on the solved values of \( x \). The final colored image will be a visually appealing pattern.

Boxed Final Answer:
\[
\boxed{\text{Solve each equation, match } x \text{ to colors, and color accordingly.}}
\]