The work of a student to solve the equation 2(5y − 2) = 12 + 6y is shown below: Step 1: 2(5y − 2) = 12 + 6y Step 2: 7y − 4 = 12 + 6y Step 3: y − 4 = 10 Step 4: y = 14 Step 5: y = 7 In which step did the student first make an error and what is the correct step?
Accepted Solution
A:
We know that Step 1 is correct, because it is just a restatement of the equation. Therefore, we can eliminate Step 1:
2(5y – 2) = 12 + 6y
In Step 2, the student tried using the Distributive Property. The Distributive Property can be written as one of the two following formulas:
a(b + c) = ab + ac a(b – c) = ab – ac
In this case, we'll use the second formula. Substitute any known values into the equation above and simplify:
2(5y – 2) = 2(5y) – 2(2) 2(5y – 2) = 10y – 4
In Step 2, the student calculated 2(5y – 2) to equal 7y – 4. However, we have just proven that 2(5y – 2) is equal to 10y – 4.
The student first made an error in Step 2, and the correct step is: