Question

Determine which equations have the same solution set as 2/3-x+1/6=6x by recognizing properties rather than solving. Check all that apply.

A. 4-6x+1=36x
B. 5/6-x=6x
C. 4-x+1=6x
D. 5/6+x=6x
E. 5=30x
F. 5=42x

Answer 1

To determine which equations have the same solution set as 2/3-x+1/6=6x, we can recognize properties rather than solving the equations. By rearranging the equation and comparing it to the given equations, we can identify the equations that have the same solution set.

Step-by-step explanation:

To determine which equations have the same solution set as 2/3-x+1/6=6x, we need to recognize properties rather than solving the equations. We can do this by rearranging the equation and comparing it to the given equations:

2/3-x+1/6=6x

Rearranging, we get 1/6 + 2/3 - x = 6x

Now let's compare it to the given equations:

• A. 4-6x+1=36x: This equation does not have the same solution set.
  
• B. 5/6-x=6x: This equation does have the same solution set.
  
• C. 4-x+1=6x: This equation does not have the same solution set.
  
• D. 5/6+x=6x: This equation does not have the same solution set.
  
• E. 5=30x: This equation does not have the same solution set.
  
• F. 5=42x: This equation does not have the same solution set.
  

So the equations that have the same solution set as 2/3-x+1/6=6x are B. 5/6-x=6x.