**Answer:**

Image 1 (problem 3): infinitely many solutions

Image 2 (problem 1): one solution

Image 3 (problem 2): no solution

**Step-by-step explanation:**

Image 1 (problem 3):

2x + x + 9 = 8x - 5x + 9

Combine like terms on the left.

3x + 9 = 8x - 5x + 9

Combine like terms on the right

3x + 9 = 3x + 9

Since the equations are equal, the answer to this is infinitely many solutions.

Image 2 (problem 1):

2(4x + 3) = 12x + 2 * 4x + 4

Distribute the two inside the parenthesis on the left.

8x + 6 = 12x + 2 * 4x + 4

Multiply 2 and 4x.

8x + 6 = 12x + 8x + 4

Combine like terms on the right.

8x + 6 = 20x + 4

Subtract 20x from both sides.

-12x + 6 = 4

Subtract 6 from both sides.

-12x = -2

Divide both sides by -12.

x = 1/6

Since x comes out to a specific value, the answer is one solution.

Image 3 (problem 2):

54x + 1906x - 64 = 49(40x + 65)

Combine like terms on the left.

1960x - 64 = 49(40x + 65)

Distribute the 49 into the parenthesis on the right.

1960x - 64 = 1960x + 3185

This equation has no solution as you cannot subtract 1960x from both sides as that would eliminate the variable and since you cannot do that, you cannot progress in solving it.