Variables – Practice Problems

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In math, you often use variables: letters of the alphabet (and sometimes even Greek letters) that represent an unknown value, or a quantity that can vary.

With variables, you can represent variable quantities, such as a price that varies, the number of items you wish to buy, or a gym membership where the overall costs vary depending on the number of months you are willing to be a member, and so on.

So in math, expressions and equations often use variables. But variables are also fundamental components of functions, where one input, x, has only one output, usually y. Any letter or symbol can represent a variable, or unknown, as they're sometimes called; it makes no difference whether you use a, k or x.

But there are some conventions in math. Certain variables are used in specific contexts, like y = mx + b or ax² + bx + c in Algebra. For example, in Geometry, Greek letters are often used for angles, capital letters are used for vertices and lowercase letters are used for sides.

In mathematical rules, laws, theorems, and standardized formulas, x usually represents the unknown value you have to solve for, while variables like a, b, c, or m are used as parameters or coefficients, where the rule always works the same, no matter which integer or real number you substitute in. In functions, you'll find that x and y are used most of the time, where y stands for a value that depends on the value of the variable x.

Interpret the structure of expressions. CCSS.MATH.CONTENT.HSA.SSE.A.1

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Exercises in this Practice Problem
Complete the definition of a variable.
Find the appropriate expression that describes the cost of Sarah's mobile phone service.
Calculate which rate plan is better for Sarah.
Calculate the value for the variable $x$.
Determine which of the following are variables.
Identify the correct value for $x$ for each equation.