Equations
We are given the equation:
50 + 1 = 51
Which is obviously true.
a. Adding 12 to each side of the equation:
50 + 1 + 12 = 51 + 12
Operating:
63 = 63
Which is also true.
b. Adding 10 + 2 to the left side of the equation and 12 to the right side:
50 + 1 + 10 + 2 = 51 + 12
Operating:
63 = 63
The resulting equation is true.
c. Now we add the equation 4 + 3 = 7 to the first equation 50 + 1 = 51. Adding the left side and the right side independently:
50 + 1 + 4 + 3 = 51 + 7
Operating:
58 = 58
The resulting equation is true
2. We can add any equation to 50 + 1 = 51 in such a way that the resulting equation is true, as long as the new equation to add is also true.
For example, add 10 + 20 = 5 + 5 + 10 + 10 to 50 + 1 = 51
Since both equations are true, we expect to have a true equation as a result:
10 + 20 + 50 + 1 = 5 + 5 + 10 + 10 + 50 + 1
Operating:
81 = 81
The resulting equation is true.
3. If we add a false equation to our given equation, the result is also a false equation. For example, add 12 = 10 + 1 to 50 + 1 = 51:
50 + 1 + 12 = 51 + 10 + 1
Operating:
63 = 62
This equation is false because we added a false equation to a true equation