Chapter 5: Algebra

A notepad displays four equations. The first equation reads, 2 plus x equals 5. Below that is a second equation that reads x equals 3. The third equation reads, 3 plus x equals 8. Below that is a fourth equation that reads x equals 5. A pen rests on top of the notepad. — **Figure 5.1** In these algebraic equations, the $x$ represents different numbers.In these algebraic equations, the $x$ represents different numbers. (credit: Larissa Chu, CC BY 4.0)

The jump from arithmetic to algebra can be a difficult one for many students. Many students struggle with the idea that mathematics can include situations that aren’t static and do change. In elementary arithmetic, a situation such as: $5 + 3 =____$

is a static situation and will yield the answer of 8 every time. However, a situation such as: $5 x + 3 =____$

can yield many different answers because the answer depends on what amount (number) that $x$ represents. Since the value of $x$ can vary (represent different values), it is known as a variable.

Adapted from Contemporary Mathematics by OpenStax (openstax.org), licensed under CC BY-NC-SA 4.0. Changes were made. License: CC-BY-NC-SA-4.0.