Question

The work of a student to solve the equation 3(3x − 4) = 8 + 2x + 5 is shown below: Step 1. 3(3x − 4) = 8 + 2x + 5 Step 2. 6x − 7 = 13 + 2x Step 3. 6x − 2x = 13 + 7 Step 4. 4x = 20 Step 5. x = 5 In which step did the student first make an error and what is the correct step? (1 point) Step 2, 9x − 12 = 13 + 2x Step 2, 9x − 4 = 2(6 + x + 3) Step 3, 6x + 2x = 13 + 7 Step 3, 6x − 2x = 13 − 7

Answer 1

(a) Step 2. 9x -12 = 13 +2x

Explanation:

The distributive property says a factor outside parentheses multiplies each term inside parentheses. It is an error to do addition of the factor, or to miss multiplying a term.

In Step 2 of this "solution", the factor of 3 is erroneously added to each coefficent inside parentheses. It should be multiplied.

Correct Step 2: 9x -12 = 13 +2x

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The rest of the solution should be ...

Step 3: 9x -2x = 13 +12

Step 4: 7x = 25

Step 5: x = 25/7

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Check

3(3(25/7) -4) = 8 + 2(25/7) +5

3((75 -28)/7) = 13 +50/7

141/7 = 141/7 . . . . . answer checks OK