An unknown equation, the degree of which is 1, and the left and right are equal, is called a one-dimensional linear equation. The solution of its equation is called the solution of this equation.

Solution steps

1. Denominator removal: multiply each term on both sides of the equation by the least common multiple of each denominator;

Basis: Attribute II of the equation

Second, remove the brackets.

Generally, the brackets are removed first, then the brackets are removed, and finally the braces are removed, according to the law of multiplication distribution (remember to change the number if there is a minus sign or a division sign outside the brackets).

Fundamentals: laws of multiplication and distribution

Third, mobile projects.

Practice: move all the items with unknowns in the equation to one side of the equation (in general, the items with unknowns are moved to the left of the equation and the constant items are moved to the right).

Basis: Attribute of equation 1

Fourth, merge similar items.

Practice: Transform the equation into the form of ax=b(a≠0);

Fundamentals: Multiplication distribution law (inverse multiplication distribution law)

5. The coefficient is 1.

Practice: divide the unknown coefficient a on both sides of the equation to get the solution of equation x = b/a.

Basis: the properties of the equation II.

Formula for solving equation

Denominators are removed, brackets are removed, terms are shifted, signs are changed, similar terms are merged, and then coefficients are removed.

Homotopy equation

If the solutions of two equations are the same, then these two equations are called homosolution equations.

Same solution principle

Add or subtract the same number or the same equation from both sides of the (1) equation, and the obtained 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.

Root formula

Because linear equation is a basic equation, the only solution in the textbook is the above method.

However, for the standard linear equation: ax+b=0 (a≠0).

The formula for finding the root can be obtained.

Function solution

Since the linear function of one variable can be transformed into the form of ax+b=0 (A, B is constant and a≠0), solving the linear equation of one variable can be transformed into:

When a function value is 0, find the value of the corresponding independent variable. From the image, this is equivalent to finding the value of the abscissa of the intersection of a straight line y=kx+b(k, b is a constant, k≠0) and the X axis.

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