Final answer:
The equation that has the same solution set as 2/3 - x + 1/6 = 6x is c) 2/3 - x - 1/6 = 6x.
Step-by-step explanation:
To determine which of the choices has the same solution set as the equation 2/3 - x + 1/6 = 6x, we can simplify the given equation and compare it to each choice.
First, let's simplify the equation:
2/3 - x + 1/6 = 6x
Combining -x and 6x, we get -x + 6x = 2/3 + 1/6
Simplifying further, we have 5x = 2/3 + 1/6
Now, let's compare this simplified equation to each choice:
a) 2/3 - x + 1/6 = 6x: This choice is not the same as the simplified equation.
b) 2/3 + x + 1/6 = 6x: This choice is not the same as the simplified equation.
c) 2/3 - x - 1/6 = 6x: This choice is the same as the simplified equation, as it has -x - 1/6 on the left side.
d) 2/3 + x - 1/6 = 6x: This choice is not the same as the simplified equation.
Therefore, the equation that has the same solution set as 2/3 - x + 1/6 = 6x is c) 2/3 - x - 1/6 = 6x.