Final answer:
Only one equation, namely Equation A) 1 + 3x - 6 = 16, is equivalent to 1+3(x-2)=16. The other provided options do not represent the same equation after applying proper algebraic distribution and simplification.
Step-by-step explanation:
The student is asking which three equations are equivalent to 1+3(x-2)=16. To find the equivalent equations, we need to distribute the 3 across the parentheses in the original equation, which gives us 1 + 3x - 6. Now let's equate this expression to each of the other sides of the equations provided in the options.
Equation A) becomes 1 + 3x - 6 = 16, which is the same as the original equation after the distribution is done. Equation B) has a different total on the right side, which is 0, so it can't be equivalent. Equation C) changes the total on the right side to 10, which isn't the same as the original total of 16, so this is not equivalent either. Equation D) and Equation E) do not correctly apply the distributive property (as they haven't subtracted the proper amount, 6, after distributing 3), so they are not equivalent. Finally, Equation F) combines the correct expression on the left, but the total on the right side is 10, again not matching the original 16.
Therefore, the three equivalent equations to 1+3(x-2)=16 are:
- Equation A) 1 + 3x - 6 = 16
- None of the other equations (B, C, D, E, F) are equivalent.
So only one of the provided equations is actually equivalent to the original equation.