# Word Problems

# Inequalities

We have four possible inequality signs to choose from: <, >, ≤, and ≥. There is also the slightly less popular ^, which means that everything below is greater than everything above, but that brings us into a touchy area, spiritually speaking. Translating English into one of these symbols is a matter of common sense. Good thing you have some of that.

The signs < and > are usually straightforward.

- "Three is less than
*x*'' can be abbreviated by 3 <*x*.

- "5 is more than
*x*'' can be written in symbols as 5 >*x*.

When we're translating into statements that use ≤ or ≥, we have a slightly wider range of English phrases to use. For example, each of the following English statements translates into symbols as *x* ≤ 20.

*x*is**less than or equal to**twenty.

*x*is**at most**twenty.

*x*is**not more than**twenty.

*x*is**not greater than**twenty.

- Twenty could be more than
*x*, could be exactly as much as*x*. You'll never know. Na-nana-boo-boo.

Each of these following English statements translates into symbols as *x* ≥ 0.

*x*is**greater than or equal to**zero.

*x*is**not less than**zero.

*x*is**not smaller than**zero.

*x*is**at least**zero.