1. At the same time, add or subtract the same number on both sides of the equation, and the new equation has the same solution as the original equation.
2. Both sides of the equation are multiplied and divided at the same time and the same number (0 out) is subtracted. The new equation has the same solution as the original equation.
Such as 7X- 12=3X+4.
We use the first homosolution principle to subtract 3X from both sides of the equation.
Then the left one is 7X- 12-3X, and the calculated one is 4x-12;
3X+4-3X on the right, 4 after calculation.
So the original equation becomes 4X- 12=4.
Let's use the first same solution principle, and add 12 to both sides of the equation.
On the left is 4X- 12+ 12, which is the calculated 4X.
4+ 12 on the right, and calculate 16.
So the original equation becomes 4X= 16.
We use the second same solution principle, and divide both sides of the equation by 4.
On the left is 4X÷4 4, the calculated X.
16÷4=4 on the right
So the original equation becomes X=4, which is the "solution" (that is, the root) we want.
Because the above process is too complicated, we simplify it and call it "moving goods". Usually we move the term with unknown number to the left of the equal sign and the constant to the right of the equal sign. It is important to note that the moved term must change its attribute flag! Take the above as an example:
7X- 12=3X+4
Transferred items: 7X-3X=4+ 12 (see? 3X becomes-3x; -12 becomes+12)
Calculate 4X= 16 on both sides.
X=4 when both sides are divided by 4 at the same time.
Solving the equation is as simple as that.