Properties of equality
We are given the equation:
7 ( x - 1 ) = 2 ( 3x + 2 )
The first step is to apply the distributive property:
7 x - 7 = 6x + 4
Answer for label 4 of the table: Distributive property
Now to eliminate the 7x, we apply the subtraction property:
7 x - 7 - 7x = 6x + 4 -7x
Simplifying:
-7 = -1x +4
Answer for label 5 on the table: Subtraction property
Now to leave the variable alone, we apply the subtraction property again.
Subtracting 4:
-7 - 4 = -1x + 4 - 4
Simplifying:
-11 = -1x
Answer for label 6 on the table: Subtraction property
Now we apply the division property to let the x without any coefficient:
Dividing by -1:
-11 / (-1) = -1x / (-1)
Operating:
11 = x
Answer for label 7 on the table: 11 = x
Finally, the reflexive property gives us the final answer:
if 11 = x, then x=11
Answer for label 8 on the table : x = 11
Note: The last step should have been better called the symmetric property:
if A=B, then B=A. That was exactly what we did as the final step