Math Coloring Pages from Coloring Squared - Free Printable

To solve this "Color by Number" puzzle, we need to find the value of $x$ for each equation. Then, we match that number to the color key provided in the image.

The Color Key:
* 3 = Blue
* 4 = Pink
* 5 = Purple
* 6 = Red
* 7 = Green
* 8 = Orange
* 9 = Yellow

*(Note: The center star is already labeled "Red".)*

Here are the step-by-step solutions for each section of the mandala, moving clockwise from the top right:

1. Equation: $60 + 2x = 74$
* Subtract 60 from both sides: $2x = 14$
* Divide by 2: $x = 7$
* Color: Green

2. Equation: $88 - 5x = 53$
* Subtract 88 from both sides: $-5x = -35$
* Divide by -5: $x = 7$
* Color: Green

3. Equation: $103 - 8x = 79$
* Subtract 103 from both sides: $-8x = -24$
* Divide by -8: $x = 3$
* Color: Blue

4. Equation: $1x + 64 = 67$
* Subtract 64 from both sides: $x = 3$
* Color: Blue

5. Equation: $23 + 4x = 55$
* Subtract 23 from both sides: $4x = 32$
* Divide by 4: $x = 8$
* Color: Orange

6. Equation: $-4x + 49 = 29$
* Subtract 49 from both sides: $-4x = -20$
* Divide by -4: $x = 5$
* Color: Purple

7. Equation: $31 + 4x = 55$
* Subtract 31 from both sides: $4x = 24$
* Divide by 4: $x = 6$
* Color: Red

8. Equation: $129 + -13x = 38$ (which is $129 - 13x = 38$)
* Subtract 129 from both sides: $-13x = -91$
* Divide by -13: $x = 7$
* Color: Green

9. Equation: $-110 - 8x = -70$
* Add 110 to both sides: $-8x = 40$
* Divide by -8: $x = -5$
* *Wait, looking closer at the image text:* It says `-110 - 8x = -70`. Let's re-read carefully. Ah, typically these puzzles result in positive integers 3-9. Let me re-examine the equation in the image. It looks like `110 - 8x = 70` or similar? No, it clearly has negative signs. Let's look at the neighbor: `-4x = 71 = 43`. That one is weirdly written. Let's look at the bottom left sector: `-4x = 71 = 43` is likely `-4x + 71 = 43`.
Let's re-evaluate the bottom-left cluster carefully.

Let's restart the bottom-left quadrant calculations to ensure accuracy.

Bottom Left Sector:
* Equation: $-4x + 71 = 43$
* Subtract 71: $-4x = -28$
* Divide by -4: $x = 7$
* Color: Green

* Equation: $32 + 4x = 60$
* Subtract 32: $4x = 28$
* Divide by 4: $x = 7$
* Color: Green

* Equation: $-1x + 21 = 18$
* Subtract 21: $-x = -3$
* Multiply by -1: $x = 3$
* Color: Blue

* Equation: $71 + 1x = 74$
* Subtract 71: $x = 3$
* Color: Blue

* Equation: $48 + 1x = 56$
* Subtract 48: $x = 8$
* Color: Orange

Left Side Sector:
* Equation: $120 + 7x = 85$ -> This results in a negative number. Let me re-read the image. Ah, it is likely $120 - 7x = 85$? Or maybe $12 + 7x$? Looking at the font, it looks like `120`. If $120 - 7x = 85$, then $-7x = -35$, so $x=5$. If it is plus, $7x = -35$, $x=-5$. Given the pattern, it is almost certainly subtraction or a typo for a smaller number. However, looking at the previous equation $48+1x=56$, the numbers are consistent. Let's look at the equation above it: `39 + 3x = 54`. $3x=15, x=5$. The one below is `120 + 7x = 85`. This is physically impossible for positive x. Let's assume it is a typo for $12 + 7x = 85$? No, $7x=73$. How about $20 + 7x = 85$? $7x=65$. No. How about $120 - 7x = 85$? $35 = 7x$, $x=5$. This fits the "Purple" theme of that ring segment often found in these symmetrical designs. Let's assume the sign is a minus or the first number is different. Actually, looking really closely at the crop, it might be $15 + 7x = 85$? No. Let's look at the symmetry. The opposite side is $23+4x=55$ ($x=8$).
Let's look at the equation again: `120 + 7x = 85`. Is it possible it is `12 + 7x = 54`? No.
Let's look at the equation `75 + 2x = 81`. $2x=6, x=3$.
Let's look at `5x - 12 = 28`. $5x=40, x=8$.
Let's look at `71 + 3x = 86`. $3x=15, x=5$.
Let's look at `-9 + 4x = 15`. $4x=24, x=6$.
Let's look at `39 + 3x = 54`. $3x=15, x=5$.

Okay, let's re-read the problematic one: `120 + 7x = 85`. It is highly probable that this is a typo in the worksheet for $12 + 7x = 82$ ($x=10$, no) or $15 + 7x = 50$...
Actually, let's look at the visual pattern. The section corresponding to `120+7x` is adjacent to `39+3x=5` (Purple) and `48+1x=8` (Orange).
Let's try solving for $x=5$ (Purple): $120 + 35 = 155 \neq 85$.
Let's try solving for $x=3$ (Blue): $120 + 21 = 141 \neq 85$.
Let's try solving for $x=8$ (Orange): $120 + 56 = 176 \neq 85$.

Wait, could it be $12 + 7x = 85$? $7x = 73$. No.
Could it be $1.20$? No.
Could it be $120 - 7x = 85$? $35 = 7x \rightarrow x = 5$. This yields an integer. In many printed worksheets, a dash can look like a plus if blurry, or vice versa. Given $x=5$ is a valid color (Purple), and it fits the integer constraint, I will proceed with $x=5$ (Purple) assuming a typo for subtraction.

Let's check the other potentially ambiguous one: `-110 - 8x = -70`.
$-8x = 40 \rightarrow x = -5$. Again, negative.
If it were $110 - 8x = 70$: $40 = 8x \rightarrow x = 5$.
If it were $-110 + 8x = -70$: $8x = 40 \rightarrow x = 5$.
It seems the bottom-left area heavily features the answer 5 (Purple) or 7 (Green).
Let's look at the equation next to it: `-4x + 71 = 43`. We solved this as $x=7$ (Green).
The equation below that: `32 + 4x = 60`. We solved this as $x=7$ (Green).

So the wedge containing `-110...` and `-4x+71...` and `32+4x...` seems to be Green/Purple.
If `-110 - 8x = -70` is actually `110 - 8x = 70`, then $x=5$ (Purple).

Let's double check the equation `76 + -4x = 40` (Left middle).
$76 - 4x = 40 \rightarrow -4x = -36 \rightarrow x = 9$.
Color: Yellow.

Let's double check `6 + 3x = 18` (Bottom left inner).
$3x = 12 \rightarrow x = 4$.
Color: Pink.

Let's double check `29 + 5x = 44` (Bottom left inner).
$5x = 15 \rightarrow x = 3$.
Color: Blue.

Let's double check `5 + 3x = 23` (Bottom left inner).
$3x = 18 \rightarrow x = 6$.
Color: Red.

Let's double check the very bottom one: `129 + -13x = 38`.
$129 - 13x = 38 \rightarrow -13x = -91 \rightarrow x = 7$.
Color: Green.

Let's re-verify the right side.
Top Right Inner: `122 + -12x = 38`? Or `122 - 12x = 38`?
$122 - 38 = 84$. $84 / 12 = 7$.
$x = 7$.
Color: Green.

Next one clockwise: `33 - 3x = 15`.
$-3x = -18 \rightarrow x = 6$.
Color: Red.

Next: `74 - 13x = 35`.
$-13x = -39 \rightarrow x = 3$.
Color: Blue.

Next: `2x + 18 = 26`.
$2x = 8 \rightarrow x = 4$.
Color: Pink.

Next: `65 + -4x = 29`.
$65 - 4x = 29 \rightarrow -4x = -36 \rightarrow x = 9$.
Color: Yellow.

Next: `18 + -2x = 12`.
$18 - 2x = 12 \rightarrow -2x = -6 \rightarrow x = 3$.
Color: Blue.

Next: `71 - 4x = 39`.
$-4x = -32 \rightarrow x = 8$.
Color: Orange.

Summary of Colors by Section (Clockwise from Top):

1. Top Point (Star): Red (Given)
2. Top Right Outer Tip ($60+2x=74$): Green ($x=7$)
3. Top Right Middle Arc ($88-5x=53$): Green ($x=7$)
4. Top Right Inner Petal ($122-12x=38$): Green ($x=7$)
5. Right Upper Outer Tip ($103-8x=79$): Blue ($x=3$)
6. Right Upper Middle Arc ($1x+64=67$): Blue ($x=3$)
7. Right Upper Inner Petal ($33-3x=15$): Red ($x=6$)
8. Right Lower Outer Tip ($23+4x=55$): Orange ($x=8$)
9. Right Lower Middle Arc ($-4x+49=29$): Purple ($x=5$) *(Assuming typo correction for standard integer result)*
10. Right Lower Inner Petal ($74-13x=35$): Blue ($x=3$)
11. Bottom Right Outer Tip ($31+4x=55$): Red ($x=6$)
12. Bottom Right Middle Arc ($129-13x=38$): Green ($x=7$)
13. Bottom Right Inner Petal ($2x+18=26$): Pink ($x=4$)
14. Bottom Left Inner Petal ($65-4x=29$): Yellow ($x=9$)
15. Bottom Left Middle Arc ($18-2x=12$): Blue ($x=3$)
16. Bottom Left Outer Tip ($71-4x=39$): Orange ($x=8$)
17. Bottom Left Inner Petal ($-110-8x=-70$): Purple ($x=5$) *(Assuming typo correction $110-8x=70$)*
18. Bottom Left Middle Arc ($-4x+71=43$): Green ($x=7$)
19. Bottom Left Outer Tip ($32+4x=60$): Green ($x=7$)
20. Left Lower Inner Petal ($-4x=71=43 \rightarrow -4x+71=43$ is duplicate? No, the label is on the petal. The arc is $-1x+21=18$).
Let's trace the lines carefully.
The equation $-1x + 21 = 18$ is in the arc between the tip and the inner petal.
$x=3$ (Blue).
21. Left Lower Outer Tip ($71+1x=74$): Blue ($x=3$).
22. Left Lower Middle Arc ($48+1x=56$): Orange ($x=8$).
23. Left Lower Inner Petal ($120+7x=85$): Purple ($x=5$) *(Assuming typo correction $120-7x=85$)*.
24. Left Upper Inner Petal ($75+2x=81$): Blue ($x=3$).
25. Left Upper Middle Arc ($5x-12=28$): Orange ($x=8$).
26. Left Upper Outer Tip ($39+3x=54$): Purple ($x=5$).
27. Top Left Inner Petal ($-9+4x=15$): Red ($x=6$).
28. Top Left Middle Arc ($71+3x=86$): Purple ($x=5$).
29. Top Left Outer Tip ($76-4x=40$): Yellow ($x=9$).
30. Top Center Inner Petal ($1x+38=42$? No, looks like $1x + 38 = 42$ is not there. The center star is Red. The petal surrounding the star has equations? No, the equations are in the segments radiating out.

Let's refine the list into a clean final output based on the calculated values.

Calculated Values:
* $x=3$: Blue
* $x=4$: Pink
* $x=5$: Purple
* $x=6$: Red
* $x=7$: Green
* $x=8$: Orange
* $x=9$: Yellow

Final Answer:
The solution involves solving each algebraic equation to find $x$, then coloring the section according to the key.

Key Solutions:
* Blue (3): Sections with equations $103-8x=79$, $1x+64=67$, $74-13x=35$, $18-2x=12$, $-1x+21=18$, $71+1x=74$, $75+2x=81$.
* Pink (4): Sections with equations $2x+18=26$, $6+3x=18$.
* Purple (5): Sections with equations $-4x+49=29$, $120-7x=85$ (corrected), $-110-8x=-70$ (corrected to $110-8x=70$), $39+3x=54$, $71+3x=86$.
* Red (6): Sections with equations $31+4x=55$, $33-3x=15$, $5+3x=23$, $-9+4x=15$. (Center Star is also Red).
* Green (7): Sections with equations $60+2x=74$, $88-5x=53$, $122-12x=38$, $129-13x=38$, $-4x+71=43$, $32+4x=60$.
* Orange (8): Sections with equations $23+4x=55$, $71-4x=39$, $48+1x=56$, $5x-12=28$.
* Yellow (9): Sections with equations $76-4x=40$, $65-4x=29$.