Any student begins to study this topic even in the elementary grades, when the signs "more", "less" and "equal" pass. This type of inequality and equation is one of the simplest in the entire curriculum for the entire period of study of a student and student. The solution to absolutely any equation and inequality comes down to simplifying it to a linear form. What do linear equations and inequalities look like?
In this equation, the unknown is in the first degree, which allows you to quickly and easily separate variables from constants, placing them on opposite sides of the separating sign (equality or inequality). What does a method look like that will help you easily and simply solve any linear equation?
Suppose there is an equation 3x - 89 = (5x - 32) / 2. The first thing to do is to simplify the fractional part by multiplying the entire equation by 2. Then, as a result, it turns out that 6x - 178 = 5x - 32. In fact, this is already a linear equation. Now you need to simplify it by moving all the variables to the left, and the constants to the right. As a result, it turns out that x = 146. If the factor of the variable is greater than unity, the entire linear equation should be divided into it, and in this case the necessary answer will be obtained.
The same goes for inequalities. First you need to simplify linear inequality, and then move the variables to its left side, and the constants to the right. After that, the linear inequality is again simplified so that the coefficient of the variable is equal to unity. The answer to the inequality is obtained automatically, after that it only needs to be written in the desired form (in the form of an inequality, interval or gap on the axis).
As can be understood from the above, linear equations and inequalities are very simple even for elementary school children. However, it is worth remembering that this type of equation has options.
There is such a form as linear equations with two variables. How to solve them? This is a rather laborious process. At school, similar cases begin to be encountered in high school, therefore, linear equations with two variables can be attributed to more complex topics.
Suppose there exists an equation 2x + y = 3x + 17. The first thing to do is to express one unknown quantity through another. This is done quite simply: one variable is taken out to the left, all other variables and numbers to the right; Thus, all linear equations with two variables are solved. As a result, you get an equation of the form y = x + 17. The answer is expressed by plotting this function in the coordinate system and has the form of a straight line. This is how linear equations with two variables are solved.
It is also worth noting that in addition to equations with two variables, there are similar inequalities. In contrast to equations in which the function graph is the answer, the inequality encloses its answer in the plane bounded by this graph. It is worth considering: if the inequality is strict, then the schedule is not included in the answer!
So, now you imagine how to solve linear equations and inequalities. Although this topic is simple enough to study, it is worth paying attention to, since some subtleties may not be very clear, which in the control test can lead to unpleasant errors and a decrease in the final points. A linear equation is simple, the main thing is to adhere to the necessary mathematical rules, such as dividing or multiplying the entire equation by any value, transferring the elements of the function beyond the equal sign, correctly plotting graphs, and correctly recording the answer.
Knowing how to write and solve linear equations and inequalities correctly, you can understand 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 for solving the lion's share of other equations, inequalities and problems.