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3 August, 05:26

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

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  1. 3 August, 07:30
    0
    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.
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