this subject any student begins to learn in elementary school, when passing signs "more", "less than" and "equal."This type of equations and inequalities is one of the easiest in the entire curriculum for the entire period of study students.The solution is absolutely any equation and inequality boils down to, to simplify it to a linear type.How to look linear equations and inequalities?
In this equation the unknown is in the first degree, which enables fast and easy to separate the variables constant, placing them on opposite sides of the separating plate (equality or inequality).How looks the way, which will help quickly and easily solve any linear equation?
For example, there is an equation 3x - 89 = (5x - 32) / 2.The first thing to do - is to simplify the fractional part, multiplying by 2 the entire equation.Then the result will be that the 6x - 178 = 5x - 32. In fact it is - is a linear equation.Now we need to simplify it by moving all of the variables in the left-hand side, and permanent - to the right.The result will be that x = 146. If the multiplier is greater than one variable, you should divide it all a linear equation, and in this case to obtain the necessary response.
The same goes for the inequalities.First, you need to simplify linear inequality, and after - to move the variables in its left side, and permanent - to the right.Then again, a linear inequality simplifies to a variable rate equal to unity.Response to inequality is obtained automatically, then it is only necessary to add to the desired shape (in the form of an inequality, the interval or gap on the axis).
As can be understood from the above, linear equations and inequalities is very simple, even for primary school children.However, it should be remembered that this type of equations has options.
There is a view of how linear equations with two variables.How to solve them?This is a fairly time-consuming process.At school, similar cases are beginning to face in high school, therefore, linear equations with two variables can be attributed to more advanced topics.
For example, there is an equation 2x + y = 3x + 17. The first thing to do - is to express one unknown quantity by another.This is simple enough: one variable is taken out to the left side, with all other variables and numbers - to the right;thus solved all the linear equations with two variables.As a result, you get an equation of the form y = x + 17. The answer is expressed by plotting this function in a coordinate system and a straight line.That's how to solve linear equations with two variables.
It should also be noted that in addition to the equations in two variables, there are similar disparities.In contrast to the equation, the answer to which is the graph of the function, inequality concludes its response to the plane defined by this schedule.It's worth noting that if the inequality is strict, then the graph of response is not included!
So now you imagine how to solve linear equations and inequalities.Though this issue and quite easy to learn, it is to pay attention, as some subtleties may not be too clear that the control test can cause unpleasant errors and decrease the total score.The linear equation - it's just important - required to adhere to mathematical rules, such as multiplication or division of the whole equation on any value, the transfer function of the elements of the equal sign, the correct plotting, competent response record.
Knowing how to write and solve linear equations and inequalities, you will be able to understand and more complex types of equations and inequalities.That is why this topic is considered so important - almost the cornerstone of mathematics, because the principles for solving such examples are the basis of the decision lion's share of the remaining equations, inequalities and problems.
