To create an algebraic expression, we utilize letters to represent unknown values, known as variables, and combine them using various mathematical operations.

In algebra, letters such as $x$, $y$, and $z$ denote unknown values or variables. These variables can represent numbers that are not yet determined or that may vary. For instance, to express the phrase “a number increased by 5,” we can assign the variable $x$ to the unknown number and write the expression as $x + 5$.

We employ mathematical operations—such as addition, subtraction, multiplication, and division—to manipulate these variables. For example, if we wish to express “twice a number minus 3,” we can use the variable $y$ to represent the number, resulting in the expression $2y - 3$. Here, $2y$ indicates two times the value of $y$, followed by the subtraction of 3.

In certain situations, it may be necessary to utilize multiple variables. For example, to articulate “the sum of a number and twice another number,” we can designate $a$ and $b$ for the two numbers, leading to the expression $a + 2b$.

Using letters in algebraic expressions enables us to generalize mathematical problems, making them easier to solve. This approach is also fundamental in forming equations and inequalities, which are crucial for analyzing and addressing real-world challenges.