What is the principle of solving equations? What to look for.

The principles of solving equations are shifting terms to change signs and the basic properties of equations.

1. Shifting terms to change signs: moving certain terms in an equation from one side of the equation to the other with the previous sign, and adding to subtract, subtracting to add, multiplying to divide by, and dividing to multiply.

2, the basic nature of the equation

Property 1: both sides of the equation at the same time add (or subtract) the same number or the same algebraic formula, the result is still an equation. Expressed in letters, if a=b and c is a number or an algebraic formula. Then:

Property 2: If both sides of an equation are multiplied or divided by the same non-zero number, the result is still an equation.

Expressed in letters, if a=b and c is a number or an algebraic formula (not 0). Then:

a×c=b×c

Property 3: If a=b,then b=a (symmetry of the equation).

Property 4: If a=b,b=c then a=c (transitivity of the equation).

Solving equations need to pay attention to:

1, usually set x, y, z as the unknowns, you can also set other letters, all lowercase letters can be.

2. Solving equations should be skillful in using the basic properties of equations.

3, solve the equation should be brought to the end of the results of the equation for checking, and pay attention to the number and nature of the solution: n a times the equation is to contain n unknowns, and contains the highest number of unknowns is a.

Extension

The general solution to the equation:

1, go to the denominator , equation Multiply both sides simultaneously by the least common multiple of each denominator.

2, remove the brackets , generally first remove the parentheses, then remove the parentheses, and finally remove the curly braces. But the order can sometimes be based on the situation to make the calculation simple. Can be based on the law of distribution of multiplication.

3, shift the term , the equation containing the unknown to the other side of the equation, the rest of the items to the other side of the equation to shift the term to pay attention to change the sign.

4, combining like terms, the original equation into the form ax = b (a ≠ 0).

5. Reduce the coefficients to one , divide both sides of the equation by the coefficients of the unknowns at the same time.

6. To arrive at a solution to the equation.

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