Any math curriculum includes material on inequalities.They surround the student everywhere in the formulas, axioms and algebraic problems.What is inequality and it looks like the solution of inequalities?
inequality in their condition involves the difference between the two parts of the expression.A total of two types: strict and lax.Non-strict inequality allow embodiment, wherein parts equal (in this case using the signs "is greater than or equal to" and "less than or equal to").Strict inequality does not allow the use of answers in which the parts are equal.In this case the solution of inequalities involves the signs "more," "less than" and "not equal."
In most cases inequalities have to answer a range of values, including as integers and the set of fractional.To give complete and only correct answer, write down the value is not accurate, and their intervals.Solution inequalities occurs most often by periods, where it is checked in a part of the segment coordinate all the conditions that enable a correct inequality.The answer is written in the form of "unknown origin belongs to the segment data boundaries."Example of a record response - x ∈ (7; 10], where the parentheses denotes a strict inequality, and square - lax (ie, 10 is one of the possible answers, and 7 - no). If the range of possible solutions of the inequality tends to infinity, theninfinity sign in the answer is always indicated by parentheses.
inequality may be many kinds, but the most difficult issues arise in two cases: the decision irrational and fractional inequalities.
What is irrational inequality? This inequality, one part of which is the root function.Looks this inequality is quite difficult for an inexperienced student, and for many students of mathematical departments. However, the decision irrational inequalities simple enough: you just need to build all the disparities in the extent to which originated in one of its parts. It is necessary to comply with only one rule: if onefunction is negative, in the construction of even degree distort inequality and make it different from the original by its very essence.Therefore, the decision of irrational inequalities is one of those moments in which the lion's share of examinees wrong students.
decision fractional inequalities is also quite simple.Fractional inequalities - it is, in which one of the parts is a fraction.What to do to make the right decision fractional inequalities?Simply multiply both sides of inequality by the value of the denominator of one of the functions.It will function in a simple form that allows you to quickly and easily calculate the correct range of solutions to inequality.
There are many kinds of inequalities, and the decision of many of them differ from each other.You need to know and provide the correct method for solving each of them to be able to competently make a condition, write the answer and get high scores for work.The similar decision irrational and fractional inequalities?First of all the fact that their decision to apply the simplified by abolishing the inconvenient factor (in one case - the root, the second - denominator).Therefore, every student, and the student must remember that barely noticed at the root of inequality or the denominator, it must react and either build both sides to the desired degree or multiply both sides of inequality by the denominator.This method of solution works in most cases, except for the exceptional complexity of tasks (which, incidentally, are very rare).Therefore, we can say with confidence that the solution of inequalities proposed above would be true in almost one hundred percent of the cases.Good luck in school!
