Question

Which equation has the same solution set as 2/3 - x + 1/6 = 6x?

a) 2/3 - x + 1/6 = 6x
b) 2/3 + x + 1/6 = 6x
c) 2/3 - x - 1/6 = 6x
d) 2/3 + x - 1/6 = 6x

Answer 1

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.