# Word Problems (Algebra)

## Creating Expressions, Equations, and Inequalities

One of the most critical skills in algebra is learning to write an equation.  Being able to translate a problem -- whether a word problem or a real life problem -- into an equation opens up an entire realm of math.

So, how do you translate words into an equation?

First, some basics:

## Creating Equations (Unknowns in terms of same variable)

In algebra we use variables to represent unknowns.  And, by using the tips and skills in the Creating Equations lesson, we can put together an equation from most word problems.  However, it's difficult (and sometimes impossible) to solve a single equation with two variables.  So, how can we take an equation with two unknowns and write an equation with only one variable?

Often word problems tell you how the two unknowns are related to each other, giving you a way to write one uknown "in terms of" another unknown.

## Create Equations from Word Problems

One of the algebra skills that students struggle with the most is writing equations from word problems. Ironically, translating real life problems into math is one of the key ways that algebra can become useful in real life (All those times you ask yourself, why do I need to learn this?  This is why you need to learn algebra!).

## Math Logic and Vocabulary

Math is a precise practice and getting math right often relies upon a mutual understanding.  When I say "integer," it's important that everyone understand what an integer is (it's any non-decimal number, positive, negative, or 0).

So, not only is math vocabulary critical to executing math problems, a lot of math tests ask questions that rely explicitly on vocabulary.  So, make sure that you know these terms:

## Interpret Equations

Equations are mathematical sentences.  We write equations to solve for variables that we don't know, but can predict based upon other variables. Some of the most useful -- and difficult -- math problems ask students to write or interpret equations.  What does this variable mean?  What happens to variable $n$ when variable $x$ goes up or down?