Often, in models for practical situations we do not work with linear equations exclusively; we also work with linear inequalities. For example, the fact that time #t# can not be negative, is expressed in the inequality #t\ge0#. An example of the type of inequality we are dealing with here is #4x-1\leq 7x-2#. This one is linear in x: it does not contain higher powers of #x#.

As with equations, we can also look at systems of inequalities. To formulate those solutions we use the logical operators '#\land#' for 'and' and '#\lor#' for 'or'. The solution will then take the form of \[(a\lt x\land x \lt b)\lor (c\lt x\land x\le d)\lor (x=e)\tiny,\] where #a\lt b\lt c\lt d\lt e#. In this formula #x# is greater than #a# and smaller than #b#, or greater than #c# and smaller than or equal to #d#, or equal to #e# . The 'or' is never exclusive: with #A\lor B# we always say that #A# or #B# is true, whereby it is possible that #A# and #B# are both true. In practice, the above statement is sometimes abbreviated to \[(a\lt x \lt b)\lor (c\lt x\le d)\lor (x=e)\tiny.\]

We will also look at linear inequalities with two unknowns. An example is #2x+3y-7\lt0# . On the plane the solutions of the equation #2x+3y-7=0# represent a line. The solutions to the corresponding inequality are all nodes #\rv{x,y}# on one side of that line. We can describe the solutions algebraically as all nodes #\rv{x,y}# with #x\lt{\frac{7}{2}-\frac{3}{2}y}# . Here we see #y# as a parameter and we solve the inequality as it were an inequality with the unknown #x# .