Please check my answers :).

1. Complete two column proof. Given: x/6+2=15
Prove: x=78

x/6+2=15 A:__Given____

x/6=13 B:__Addition property of Equality____

x=78 C:__Multiplication property of Equality_____

If you are balancing the equation... on line two (B) you are subtracting 2 from both sides. As long as you mean the "addition property of equaltity" + (-2) then your proof is sound.

Your answers are correct! Let's go through the steps again to understand how to arrive at the solution:

Given: x/6 + 2 = 15

Step A: Given
The original equation is given to us.

Step B: Addition property of Equality
To isolate x, we need to get rid of the constant term 2. We can use the Addition property of Equality to subtract 2 from both sides of the equation.
x/6 + 2 - 2 = 15 - 2
x/6 = 13

Step C: Multiplication property of Equality
To solve for x, we can use the Multiplication property of Equality. We can multiply both sides of the equation by 6 to get rid of the fraction.
6 * (x/6) = 13 * 6
x = 78

Therefore, your proof is correct, and x = 78 satisfies the given equation x/6 + 2 = 15. Well done!