How to solve modules?
A module is the absolute value of an expression. To somehow designate a module, it is customary to use direct brackets. That value, which is enclosed in equal brackets, is the value that is taken in modulus. The process of solving any module consists in revealing those same straight brackets that are called modular brackets in mathematical language. Their disclosure occurs according to a certain number of rules. Also, in order of solving modules, there are also sets of values of those expressions that were in modular brackets. In most cases, the module is expanded in such a way that the expression that was submodular receives both positive and negative values, including zero. If we start from the established properties of the module, different equations or inequalities from the initial expression are compiled in the process, which then need to be solved. Let's look at how to solve modules.
The solution of the module begins with the recording of the originalequations with modulus. To answer the question of how to solve equations with a module, you need to open it completely. To solve such an equation, the module is revealed. All modular expressions must be considered. It should be determined at what values of the unknown quantities that make up its composition, the modular expression in brackets turns to zero. In order to do this, it is enough to equate the expression in modular brackets to zero, and then calculate the solution of the resulting equation. The values found should be fixed. In the same way, we also need to determine the value of all the unknown variables for all the modules in the given equation. Next, we need to address the definition and consideration of all cases of existence of variables in expressions when they are different from zero. To do this, we need to write down some system of inequalities, respectively, to all the modules in the initial inequality. Inequalities must be designed so that they cover all available and possible values for a variable that are found on a number line. Then you need to draw this very numerical line for visualization, on which in the future to postpone all the received values.
Almost everything can now be done on the Internet. The module is not an exception to the rules. Solve online it can be on one of the many modern resources. All those values of the variable that are in the zeroth module will be a special constraint that will be used in the process of solving the modular equation. In the initial equation it is required to open all available modular braces, while changing the sign of the expression, so that the values of the required variable coincide with those values that are visible on the number line. The resulting equation must be solved. The value of the variable that will be received during the solution of the equation must be checked for a constraint, which is specified by the module itself. If the value of the variable fully satisfies the condition, then it is correct. All the roots that will be obtained during the solution of the equation, but will not be approached by constraints, must be discarded.