The system of inequalities is written as follows:
To solve this system of inequalities means to find the set of all acceptable values of variable satisfying each inequality of the system.
Consider an example. Suppose we have the system of inequalities:
To solve it, we will use a numerical line and draw the intervals of all acceptable values of the variable corresponding to each inequality of the system:
The blue color indicates the set of all acceptable values of the variable , which satisfy inequality , orange - inequality and green - inequality .
To find a solution to the system of inequalities, we need to combine the intervals of all acceptable values of variable which satisfy each inequality of the system. From the figure (see on the left to the right) it follows that:
The obtained result can also be graphically displayed on a numeric axis:
Our online calculator based on wolfram alpha system can solve more complex systems of inequalities than the one just discussed. Please note that the symbol ≥ must be entered in calculator as >= (in form of two characters greater and equal to), and the symbol ≤ - as <=.