ALGEBRA

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Beagleboy how do I explain that in 50 words?
Post your 50-word response to the following:

Explain why the equation -6(x + 3) = -6x + 5 has no solution and 7x +18 + 8x = 8(x + 4) + 7x – 14 has infinitely many solutions.

  • ALGEBRA -

    Can anyone help me I need to explain this problem in 50 words.

    Explain why the equation -6(x + 3) = -6x + 5 has no solution and 7x +18 + 8x = 8(x + 4) + 7x – 14 has infinitely many solutions.

  • ALGEBRA -

    solving the first gives us
    0 = 23 which is nonsense, thus no solution.

    solving the second gives us
    0 = 0 which is true, thus any value of x will work ---> an infinite number of solutions.

    In general:
    if the variable drops out, and
    -you end up with true statement --> infinite number of solutions
    -if you end up with a false statement ---> no solution.

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