1. Basis for merging similar items: 1. Combine the items with the same number of unknowns into one item by multiplication and division; Constants are combined into one item after calculation. The number of times is the same, but the coefficient is increased and decreased. The basis of 1. Transfer term: the properties of the equation 1 After the unknown term changes, it moves to the left of the equation, and the unknown term moves to the right. 3. When you move an item from one side of the equation to the other, you must change the sign (for example, change+to-and × to \ \). Properties of the property equation 1: the equation still holds when a number is added to both sides of the equation or the same number or the same algebraic expression is subtracted. Property 2 of the equation: both sides of the equation expand or contract at the same time by the same multiple (except 0), and the equation still holds. Property 3 of the equation: When both sides of the equation are multiplied (or squared) at the same time, the equation still holds. Solving the equation is based on these three properties of the equation. Editing this solution step to make the left and right sides of the equation equal is called the solution of the equation. General solution: 1. Denominator removal: multiply both sides of the equation by the least common multiple of each denominator (items without denominator should also be multiplied); Basis: Properties of Equation 2. Remove the brackets: generally, remove the brackets first, then the brackets, and finally remove the braces, according to the multiplication and division method (remember that if there is a minus sign or a division sign outside the brackets, the number must be changed). 3. Move the items in the equation: move all the items containing unknowns to one side of the equation (generally, the items containing unknowns are on the left side of the equation and the constant items are on the right side). Basis: multiplication and division (the inverse of multiplication and division) ⒌ coefficient is 1: divide the unknown coefficient a on both sides of the equation to get the solution of equation x = b/a basis: the properties of equation 2 are homotopy equations. If the solutions of two equations are the same, then these two equations are called homotopy equations. The same solution principle of the equation: 1. Adding or subtracting the same number or the same equation on both sides of the equation is the same solution equation as the original equation. 2. The equation obtained by multiplying or dividing the same number whose two sides are not zero is the same as the original equation. An important method to solve the application problem of linear equation with one variable: 1. Examine the problem carefully; 2. Analyze known quantity and unknown quantity; 3. Find a suitable equivalence relation; 3. Set a suitable unknown quantity; 3. List a reasonable equation (formula); 3. Solving equations (solving problems); 3. Test and write the answer (answer) AX = When a=0 and b=0, the equation has countless solutions (note: this situation is not a linear equation, but an identity). When a=0 and b≠0, the equation has no solution (this situation does not belong to a linear equation). For example, (3x+1)/2-2 = (3x-2)/10-(2x+3)/5. If you divide by the denominator (the least common multiple of the denominator multiplied by both sides of the equation), you get 5 (3x+65438). Unbound: 15x+5-20=3x-2-4x-6 Shift: 15x-3x+4x=-2-6-5+20 Merge similar items: 16x=7 Split into 1: x. A = BAC = BCA = BC But for the standard one-dimensional linear equation aX+b=0, we can get the root formula X=-(b/a).