Is the answer to the problem below correct? If yes, why? If not, what mistake(s) were made in solving the problem an what is the corre

Question

Is the answer to the problem below correct? If yes, why? If not, what mistake(s) were made in solving the
problem an what is the correct answer?
Step 1: 12 = -2(x – 4) – 8
Step 2: 12 = -2x – 8 – 8
Step 3: 12 = -2x – 16
Step 4: 28 = -2x
Step 5: 26 = x

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Gerda 5 years 2021-08-18T12:42:39+00:00 1 Answers 30 views 0

Answers ( )

  1. thienthi
    0
    2021-08-18T12:44:10+00:00
    Reply

    9514 1404 393

    Answer:

      x = -6 (correct answer)

      mistakes were made in Step 2 and Step 5.

    Step-by-step explanation:

    The mistake is made in Step 2, application of the distributive property. This is often a source of error. Here, the error is in signs.

    Step 1: 12 = -2(x -4) -8

    Step 2: 12 = -2x +8 -8 . . . . . . the correct step 2

    Step 3: 12 = -2x . . . . . . . . . . . like terms combined

    Step 4: -6 = x . . . . . . . . . . . . . divide by -2

    __

    Check

      12 = -2(-6 -4) -8 = -2(-10) -8 = 20 -8 = 12 . . . . answer checks OK

    __

    Comment on other mistake

    In the original Step 5, -2 was divided on the right and added on the left. This is a violation of the properties of equality, so guarantees a wrong answer. The same operation must be performed on both sides of the equation.

    An additional mistake was made in that the answer was not checked.

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )