Add (or subtract) the same number (or formula) on both sides of the equation and the result is still the same.

If a=b, then a c = b c

2. Properties of Equation 2

Multiply by the same number on both sides of the equation, or divide by the same number that is not 0, and the result is still equal.

If a=b, then AC = BC.

If a=b(c≠0), then a/c = b/c.

Properties of Equation (Exercise)

(1) Use the properties of the equation to solve the following equation:

x/2+2=6，4x-2=2

(2)x=0 and x=-2 are the solutions of which of the following equations?

5x+7=7-2x，6x-8=8x-4

(3) The number on a two-digit number is 1, and the number on the tenth digit is X. If 1 and x are reversed, the new two-digit number is smaller than the original two-digit number 18. Which equation should x be the solution of? Can you figure out what x is?

Properties of Equation (Answer and Analysis)

( 1)

answer

8, 1

analyse

Test site: the properties of equation 1 and the properties of equation 2.

Steps to solve the problem:

Solution:

x/2+2=6

Subtract 2 from both sides to get x/2+2-2=6-2.

x/2=6-2

x/2=4

Multiply both sides by 2 to get x/2×2=4×2.

x=8

Steps to solve the problem:

Solution:

4x-2=2

Add 2 to both sides to get 4x-2+2=2+2.

4x=4

Divide the two sides by 4, and you get 4x÷4 = 4÷4 = 4÷4.

x= 1

(2)

answer

X=0 is the solution of 5x+7=7-2x;

X=-2 is the solution of 6x-8=8x-4.

analyse

Test site: the properties of equation 1 and the properties of equation 2.

Steps to solve the problem:

Solution:

5x+7=7-2x

Add 2x-7 to both sides to get 5x+7+2x-7=7-2x+2x-7.

5x+2x=7-7

7x=0

x=0

Steps to solve the problem:

Solution:

6x-8=8x-4

Add 8-8x to both sides to get 6x-8x=-4+8.

-2x=4

x=-2

(3)

answer

three

analyse

Test site: the properties of equation 1 and the properties of equation 2.

Description: The number on one digit of a two-digit number is 1, and the number on the tenth digit is X, which is10x+1; Switch 1 with x, and the new number is10+x; The new two-digit number is smaller than the original two-digit number 18, and the original number = new number+18, then10x+1= (10+x)+18.

Steps to solve the problem:

Solution:

10x+ 1 =( 10+x)+ 18

10x+ 1=x+28

Subtract x+ 1 from both sides to get 10x-x=28- 1.

9x=27

x=3