Question

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

Answer 1

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.