Question

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?

Answer 1

Step 2: 10y – 4 = 12 + 6y

Answer 2

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:

Step 2: 10y – 4 = 12 + 6y

I hope this helps!