1, difference: after the difference, the sign of the difference is judged by factorization and formula, and the result is obtained.

2. Quotient (often used in algebraic expression of fractional exponential power)-analytical method-flat method; Molecules (or denominator) are physical and chemical; Using the monotonicity of function (seeking the middle or scaling method) image method.

3. Comparative method (differential commercial method) is the most basic method.

Precautions:

I. Symbols:

1, add and subtract the same number or formula on both sides of the inequality, and the direction of the inequality remains unchanged.

2. When both sides of the inequality multiply or divide the same positive number, the direction of the inequality remains unchanged.

3. When both sides of inequality are multiplied or divided by the same negative number, the direction of inequality changes.

Second, the solution set:

1 greater than these two values is greater than the larger value (whichever is greater).

2. If it is less than two values, it is less than the smaller value (the same as the smaller value).

3, greater than big, less than small, no solution (big and small are not desirable).

4, bigger than the small one, smaller than the big one, and there is a solution in the middle (the small one takes the middle).

5. An inequality group consisting of three or more inequalities can be analogized.

Third, the number axis method:

The solution set of each inequality is represented on the number axis, and the points on the number axis divide the number axis into several segments. If the number of lines representing the solution set on a line segment on the number axis is the same as the number of inequalities, then this line segment is the solution set of the inequality group. Take as much as you have.

When determining the unary quadratic inequality, a >: 0, δ = b 2-4ac > 0, you can find the set of inequality solutions by "greater than taking both sides and less than taking the middle".