JoeyyTheWerido
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On a recent exam, a student was asked to simplify the expression:

12(8x − 4y) − 3(12y + 9x)

Their work is shown below:
Step 1: 12(8x − 4y) − 3(12y + 9x)
Step 2: 96x − 48y − 36y + 27x
Step 3: 96x + 27x − 48y − 36y
Step 4: (96x + 27x) + (−48y − 36y)
Step 5: 123x − 84y

Part A: In which step did they make a mistake, and what was it? (2 points)

Part B: How would you correct the mistake and solve the problem? Show all of your work. (2 points)

Respuesta :

itzamirv2

a) The mistake occurred in Step 2. In this step, the student incorrectly distributed the negative sign when multiplying -3 with 12y and 9x. The correct expression should be:

Step 2: 96x - 48y - 36y - 27x

b) To correct the mistake and simplify the expression:

Step 1: 12(8x - 4y) - 3(12y + 9x)

Step 2: 96x - 48y - 36y - 27x

Step 3: (96x - 27x) + (-48y - 36y)

Step 4: (69x - 84y)

So, the corrected expression after combining like terms is (69x - 84y)

PoumonNeedsHelp

Answer: Part A: The mistake occurred in Step 2. The student incorrectly distributed the -3 to both terms inside the parentheses of the second expression. The correct distribution should result in -36y - 27x, not -36y + 27x.

Step-by-step explanation:

Part B: To correct the mistake, the correct distribution of -3 to both terms in the second expression should be:

= 96x - 48y - 36y - 27x.

Now, combine like terms:

96x - 27x - 48y - 36y

= 96x - 27x + -48y - 36y

= 69x - 84y.

Therefore, the corrected expression is 69x - 84y

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