The module is an absolute value of number or expression. If it is required to open the module, then, according to its properties, the result of this operation always has to be non-negative.
Instruction
1. If under the sign of the module there is a number which value is known to you, then it is very simple to reveal him. Number a module, or |a|, will be equal to the most this number if an is more or equally 0. If an is less than zero, that is is negative, then its module will be equal opposite to it, that is | - a | to =a. According to this property, modules of opposite numbers are equal, that is | - a |= |a|.
2. In case submodular expression is squared or in other even degree, then it is possible just to lower module brackets as any number built in even degree is non-negative. If it is necessary to take a square root from a number square, then it will also be the module of this number therefore modular brackets can be lowered and in this case.
3. If in submodular expression there are non-negative numbers, then they can be taken out out of module limits. |c*x| =c * |x|, where with – non-negative number.
4. When the look equation | x |= |c| where x is a required variable, and with a real number takes place, it has to be opened as follows: x=+-|c|.
5. If it is necessary to solve the equation containing the module of expression which result has to be a real number, then the sign of the module open, proceeding from properties of this uncertainty. For example, if there is an expression |x-12|, then if (x-12) – non-negative, it remains invariable, that is the module will reveal as (x-12). But |x-12| will turn in (12-x) if (x-12) is less than zero. That is, the module reveals depending on value of a variable or expression in brackets. When the sign of result of expression is unknown, the task turns into the system of the equations, first of which considers the possibility of negative value of submodular expression, and the second – positive.
6. Sometimes the module can be opened unambiguously even if its value is unknown under the terms of a task. For example, if under the module there is a variable square, then the result will be positive. To the contrary, if there obviously negative expression, then the module reveals with the opposite sign.