Question

What is a variable?

Short answer

Answer: A variable is a symbol or a letter, usually from the alphabet, that represents a value that can change or vary. In mathematics, variables often represent unknown quantities or numbers, and they can play the role of placeholders. Variables are significant because they help represent unknown values, generalize relationships and patterns, formulate mathematical models, and solve problems in fields like physics, engineering, economics, and many more.

Step-by-step solution

Define Variable

A variable is a symbol or a letter, usually from the alphabet (e.g., x, y, z, a, b, c), that represents a value that can change or vary. In mathematics, variables often represent unknown quantities or numbers. Variables can also be placeholders for values that may be provided or altered within a problem.

Provide Examples

Here are some examples of variables in mathematical expressions and equations: 1) In the expression 2x + 3y, the variables are x and y. 2) In the equation x^2 + 3x + 2 = 0, the variable is x.

Explain the Significance of Variables

Variables are essential elements in mathematics and various fields such as algebra, calculus, and statistics. They help to: 1) Represent unknown values or quantities that need to be solved for. 2) Generalize relationships and patterns between quantities, like in a function y = f(x). 3) Formulate mathematical models and solve problems in fields like physics, engineering, economics, and many more. 4) Create formulas and describe a range of values for certain parameters (e.g., columns in a dataset).