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

9514 1404 393

  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

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Check

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

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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.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.