Inequalities differ from the equations not only the sign ""more"" ""/less"" standing between expressions. There are methods and the reefs.
Instruction
1. Inequalities have both a number of unique features, and the lines similar to the equations. One of the main differences imposes just so the sign ""more/less"". It means that if necessary to increase both parts by any expression (for example, by a denominator), we have to know accurately its sign (and, of course, the fact that it is not equal to zero). In particular, it needs to be considered when squaring is multiplication too. Let's look on just example. It is obvious that 3 <5. Let's increase both parts by 2. 6 <10. Still everything is right. And now we will increase by-2. Let's receive-12 <-20. And this is not right any more. Just like that it is impossible to multiply inequalities by negative numbers or expressions. In this case the sign of inequality needs to be replaced with opposite.
2. Except for this point, till a certain moment inequalities as well as the equations are solved. Reduction to a common denominator, search of the pricked-out points, transfer of members in the left part, search of roots and decomposition on multipliers. Here. Reached the most ""certain moment"" before: decomposition on multipliers. Further solutions of the equations and inequalities disperse.
3. Let's apply to the decision a method of intervals. We draw a numerical axis. On it we note an empty circle and we sign values of the pricked-out points, and painted over - not pricked out, and we begin to learn the sign of inequality in each of the received areas. For this purpose we take any point from this area (better some convenient) and we substitute in inequality into place x. As a result we receive some number. Depending on its sign we write on a numerical axis in the field ""+" or "" -"". Further it is possible to continue similar actions for other areas, and it is possible and to use cunning as there are some regularities for putting down of signs in a method of intervals: signs of areas alternate upon transition through the following point if the corresponding expression meets the point noted on a numerical axis in inequality odd number of times, and do not change upon transition through this point if even. We choose those whose sign corresponds to our inequality from all areas.
4. As a result we receive set which in the answer registers as ""X belongs..."" - dots stand still all suitable areas or points. The pricked-out points on the end of area are designated by parentheses - they do not join in the answer, not pricked out - square, and they join in the answer. Single points are designated by braces, and between areas and points be responsible as it is set, the sign of association (""U"") is put. In inequality for two variables everything the analysis of values not on a numerical axis, and on the plane is similarly, simply made.