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 x 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 x corresponding to each inequality of the system:
The blue color indicates the set of all acceptable values of the variable х, 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 х 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 <=.