Without solving, identify whether each of the following equations has a unique solution, no solution, or infinitely many solutions.

1) 3x+5 = - 2

2) 6 (x-11) = 15-4x

3) 12x+9=8x+1+4x

4) 2 (x-3) = 10x-6-8x

5) 5x+6=5x-4

Let us evaluate the equations one at a time.

1) 3x + 5 = - 2

3x = - 7

x = - 7/3

This equation has unique solution.

2) 6 (x - 11) = 15 - 4x

6x - 66 = 15 - 4x

10x = 81

x = 81/10

Ths equation has a unique solution

3) 12x + 9 = 8x + 1 + 4x

12x - 8x - 4x = 1 - 9

0x = - 8

x = - 8/0

This equation has no solution.

4) 2 (x - 3) = 10x - 6 - 8x

2x - 6 = 10x - 6 - 8x

2x - 10x + 8x = - 6 + 6

0x = 0

x = 0/0

Ths equation has no solution.

5) 5x + 6 = 5x - 4

5x - 5x = - 4 - 6

0x = - 10

x = - 10/0

This equation has no solution.