Property 1: Add (or subtract) the same algebraic expression on both sides of the equation, and the equation still holds. If a=b, then a+c = b+c;
Property 2: When both sides of the equation are multiplied or divided by the same algebraic expression that is not 0, the equation still holds. If a=b, there is a c = b c or a ÷ c = b ÷ c (c ≠ 0);
Property 3: Equation is transitive. If a 1=a2, a2=a3, a3=a4, then a 1=a2=a3=a4.
The essence and significance of equality
The properties of equations are the basis of solving equations, and many methods of solving equations should be applied to the properties of equations. If the term is shifted, the properties of the equation 1 are applied; Remove the denominator and apply Attribute 2 of the equation. By using the properties of the equation, when doing division, it should be noted that after conversion, the divisor cannot be 0, otherwise it is meaningless.
Properties of equation and matters needing attention
(1) When applying the properties of equation 1, only by adding (or subtracting) the same number or the same algebraic expression on both sides of the equation can the result be guaranteed to be an equation, and special attention should be paid to "all" and "same". If $65438 +0+x=3, add 2 on the left and 2 on the right, there will be $65438 +0+x+2 = 3 +2.
(2) When Property 2 of the equation is applied. Neither side of the equation can be divided by 0. Because 0 cannot be a divisor or denominator.
(3) The extension of equality attribute
① Symmetry: the left and right sides of the equation are interchanged, and the result is still an equation, that is, if $a=b$, then $b=a$.
② Transitivity: If $a=b$ and $b=c$, then $a=c$ (also called equivalent substitution).