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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 xx 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=____5+3=____

is a static situation and will yield the answer of 8 every time. However, a situation such as: 5x+3=____5x+3=____

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

Algebra is useful to better model real life situations. In the first equation shown, 5+3=____5+3=____ can only model situations where you add those two numbers together. For example, if your uncle gives you five dollars and your aunt gives you three dollars, then you will always receive eight dollars. The second equation 5x+3=____5x+3=____ can model more complex situations. For example, you wish to buy a game that costs $38 but you only have three dollars. Your uncle will pay you five dollars an hour to work for him. If you’ve worked five hours, have you earned enough money? If not, how many hours will you have to work?

Algebra and algebraic thinking open up a world of possibilities that arithmetic alone cannot do.

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