System of inequalities online calculator

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The system of inequalities is written as follows:

system of inequalities

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:

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:

number line with intervals of all acceptable values for variable x

The blue color indicates the set of all acceptable values of the variable х, which satisfy inequality the (x-2)(x-4) less than of equal to 0 inequality, orange - inequality the x less than 6 inequality and green - inequality the x greater than or equal to -2 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:

solution for the system of inequalities

The obtained result can also be graphically displayed on a numeric axis:

system of inequalities solution on number line

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
Solve system of inequalities:3x28x10x15


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