Algebra worksheet featuring equations with variables on both sides, showing problems, answer choices, and color-coded correct solutions.

I'll solve this step by step.

First, I need to understand what the image is showing. It appears to be a worksheet titled "EQUATIONS ON BOTH SIDES" with 10 problems that require solving equations. Each problem has three answer columns (Answer 1, Answer 2, Answer 3) and corresponding color codes for each answer.

Let me examine each problem one by one to determine which answer is correct and what color should be used according to the instructions.

Starting with Problem 1:
- Equation: 3x + 5 = 2x + 12 + 4x
- Let's solve: 3x + 5 = 6x + 12
- Subtract 3x from both sides: 5 = 3x + 12
- Subtract 12 from both sides: -7 = 3x
- Divide by 3: x = -7/3

Looking at the answers provided:
- Answer 1: No Solution
- Answer 2: Infinite
- Answer 3: x = 7

None of these match my calculation of x = -7/3. Let me double-check my work.
Actually, let me re-solve this carefully:
3x + 5 = 2x + 12 + 4x
3x + 5 = 6x + 12
5 - 12 = 6x - 3x
-7 = 3x
x = -7/3

This still doesn't match any of the given answers. Let me check if I'm misreading the equation or if there's an error in the worksheet.

Actually, let me look more carefully at the structure. The worksheet seems to be designed so that for each problem, one of the three answers is correct, and students are supposed to color the box with the correct answer according to the color code.

Let me solve Problem 2 to see if I can find a pattern:
- Equation: 5x + 4 = 2x + 16
- Subtract 2x from both sides: 3x + 4 = 16
- Subtract 4 from both sides: 3x = 12
- Divide by 3: x = 4

Looking at the answers:
- Answer 1: x = 20/7
- Answer 2: x = 4
- Answer 3: x = 7

Answer 2 (x = 4) is correct, and it's colored GREEN.

Let me continue with Problem 3:
- Equation: 3x + 15 = 2(2x + 2)
- Expand right side: 3x + 15 = 4x + 4
- Subtract 3x from both sides: 15 = x + 4
- Subtract 4 from both sides: 11 = x
- So x = 11

Looking at the answers:
- Answer 1: x = 11
- Answer 2: x = 1/3
- Answer 3: x = -2

Answer 1 (x = 11) is correct, and it's colored YELLOW.

Problem 4:
- Equation: 2x - 3 = 4x - 15
- Subtract 2x from both sides: -3 = 2x - 15
- Add 15 to both sides: 12 = 2x
- Divide by 2: x = 6

Looking at the answers:
- Answer 1: x = -2
- Answer 2: x = 3/2
- Answer 3: x = 6

Answer 3 (x = 6) is correct, and it's colored BROWN.

Problem 5:
- Equation: 2x - 3 = (4x + 9)
- This appears to be: 2x - 3 = 4x + 9
- Subtract 2x from both sides: -3 = 2x + 9
- Subtract 9 from both sides: -12 = 2x
- Divide by 2: x = -6

Looking at the answers:
- Answer 1: x = -1
- Answer 2: x = 1/2
- Answer 3: x = -6

Answer 3 (x = -6) is correct, and it's colored DARK BLUE.

Problem 6:
- Equation: 4(4x + 3) = 2x + 24
- Expand left side: 16x + 12 = 2x + 24
- Subtract 2x from both sides: 14x + 12 = 24
- Subtract 12 from both sides: 14x = 12
- Divide by 14: x = 12/14 = 6/7

Looking at the answers:
- Answer 1: No Solution
- Answer 2: Infinite
- Answer 3: x = 1.5 = 3/2

None of these match my calculation of x = 6/7. Let me double-check:
16x + 12 = 2x + 24
14x = 12
x = 12/14 = 6/7

This still doesn't match. Let me check if I'm reading the equation correctly. Maybe it's 4(4x + 3) = 2(x + 24)? That would be different.

Actually, looking at the answer choices, "No Solution" and "Infinite" suggest this might be a special case. Let me re-examine:
If I made an error in the equation... Let me try solving it again carefully.
4(4x + 3) = 2x + 24
16x + 12 = 2x + 24
14x = 12
x = 6/7

This is still not matching any of the given answers. Perhaps there's a typo in the worksheet or I'm misinterpreting something.

Let me move on to Problem 7:
- Equation: 20 - 6x + 4x - 15
Wait, this doesn't look like an equation. It should have an equals sign. Looking at the format, it might be 20 - 6x = 4x - 15?
Let me assume that's the case (since it's missing the equals sign).
20 - 6x = 4x - 15
Add 6x to both sides: 20 = 10x - 15
Add 15 to both sides: 35 = 10x
Divide by 10: x = 3.5 = 7/2

Looking at the answers:
- Answer 1: x = 0.4
- Answer 2: x = 3.5
- Answer 3: x = 3/2

Answer 2 (x = 3.5) is correct, and it's colored PURPLE.

Problem 8:
- Equation: 9x - 9 = 3x - 12 + 5x
- Simplify right side: 9x - 9 = 8x - 12
- Subtract 8x from both sides: x - 9 = -12
- Add 9 to both sides: x = -3

Looking at the answers:
- Answer 1: x = -1
- Answer 2: x = 3
- Answer 3: x = 3/7

None of these match my calculation of x = -3. Let me double-check:
9x - 9 = 3x - 12 + 5x
9x - 9 = 8x - 12
x = -3

This still doesn't match. There might be an error in the worksheet.

Problem 9:
- Equation: 2 + 5(3x + 5) = 3x
- Expand left side: 2 + 15x + 25 = 3x
- Simplify: 15x + 27 = 3x
- Subtract 3x from both sides: 12x + 27 = 0
- Subtract 27 from both sides: 12x = -27
- Divide by 12: x = -27/12 = -9/4 = -2.25

Looking at the answers:
- Answer 1: x = 7
- Answer 2: x = -4
- Answer 3: x = -6

None of these match my calculation of x = -9/4. Let me double-check:
2 + 5(3x + 5) = 3x
2 + 15x + 25 = 3x
15x + 27 = 3x
12x = -27
x = -27/12 = -9/4

This still doesn't match.

Problem 10:
- Equation: 2(x + 4) + 2(8 - x) - 2x
Again, this looks like an expression, not an equation. Assuming it's equal to something... perhaps 0? Or maybe it's 2(x + 4) + 2(8 - x) = 2x?
Let me assume 2(x + 4) + 2(8 - x) = 2x
Expand: 2x + 8 + 16 - 2x = 2x
Simplify: 24 = 2x
x = 12

Looking at the answers:
- Answer 1: x = 24
- Answer 2: x = 4
- Answer 3: x = 6

None of these match my calculation of x = 12.

After going through all the problems, I notice that Problems 1, 6, 8, 9, and 10 don't seem to have correct answers among the options provided, or I may be misinterpreting the equations. However, for Problems 2, 3, 4, 5, and 7, I was able to find the correct answers that match the given options.

The worksheet appears to be designed for students to solve equations and then color the correct answer box according to the color code. For the problems where I could verify the correct answer, here's what should be colored:

- Problem 2: Answer 2 (x = 4) should be colored GREEN
- Problem 3: Answer 1 (x = 11) should be colored YELLOW
- Problem 4: Answer 3 (x = 6) should be colored BROWN
- Problem 5: Answer 3 (x = -6) should be colored DARK BLUE
- Problem 7: Answer 2 (x = 3.5) should be colored PURPLE

For the other problems, there may be errors in the worksheet or I may be misinterpreting the equations as they're written.