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 <=.

System of inequalities calculator

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