Inequalities help us impose limits in a world in which perfect precision is not possible.
For example, let's say that we want to get as many donuts as possible while not going over $10. Let's say each donut costs $.79. Then we want to find an positive integer {$$}n{/$$}such that {$$}n*0.79 < 10{/$$}. Solving the for {$$}n{/$$}. We will go over such problems and expand on them in some depth in the first two sections.
We explore a classic inequality called the triangle inequality. It is the algebraic expression of the basic idea that going along the other two sides of a triangle takes longer than going along the third side.
We spend a few sections on absolute values. Absolute values seem fairly harmless at first as it seems we are just erasing negative signs. But it quickly gets difficult with variables involved.
We end with extending the idea of absolute value to that of a more general notion of distance.