Question

An equation and the steps to solve it are shown below: 7x − one over two (8x + 4) = 6 Step 1: 7x − 4x − 2 = 6 Step 2: 3x − 2 = 6 Step 3: 3x − 2 + 2 = 6 Step 4: 3x = 6 Step 5: x = 2 Which step was the error made and why?

Answer 1

7x − (1/2)(8x + 4) = 6
Step 1: 7x − 4x − 2 = 6
Step 2: 3x − 2 = 6
Step 3: 3x − 2 + 2 = 6
Step 4: 3x = 6
Step 5: x = 2

The error is in step 3, where 2 was added to the left side but not to the right side. The additive property of equality states that you can add the same number to both sides of an equation. Here 2 was added only to the left side. That is incorrect. 2 should have been added to both sides.
3x - 2 + 2 = 6 + 2
3x = 8
x = 8/3
The correct solution is x = 8/3, not x = 2.