Identities: One solution, no solution, or infinitely many solutions?

Up to 10 solutions

x^10 + 7x^8 - 4x^5 + 3x^3 - 6x^2 + 2x -12 = 0

two solutions

x^2 + 7x + 12 = 0

up to 3 solutions

x^3 + 2x^2 - 5x + 7 = 0

infinitely many solutions

2x + 8 = 2(x + 4)

infinitely many solutions

2x - x + 7 = x + 3 + 4

one solution

3(x - 1) = 2x + 9

infinitely many solutions

3x + 1 = 1 + 3x

no solution

3x + 7x + 7 = 2(5x + 1)

one solution

3x - 2x = 2x - 3x

no solution

4(2x + 1) = 5x + 3x + 9

one solution

4(x + 1) = x - 2

infinitely many solutions

4(x + 3) = 4x + 12

no solution

4x + 1 = 2(2x + 3)

one solution

4x + 2x + 2 = 3x - 7

one solution

4x + 2x - 5 = 7x - 1

infinitely many solutions

5(x + 2) - 3x = 2(x + 5)

infinitely Many solutions

6(x + 1) + 5 = 13 - 2 + 6x

one solution

8(x + 2) = 2x + 16

one solution

8x + 16 = -8(x - 2)

one solution

-12x + 2 = 12x + 2

no solution

-2(x + 1) = -2x + 5

one solution

.43 - (x + 12) = -3x + 6.21

infinitely many solutions

10 + x = x + 10

infinitely many solutions

2(3x + 3) = 3(2x + 2)

no solution

x + 2x + 7 = 3x - 7

no solution

x + 2x + 7 = 3x - 9

no solution

x + 5x + 4 = 3(2x - 1)

no solution

x + x + x + x = 4x + 3