Question

Which of the following algebraic expressions are literal expressions?$$5 x y-2 x$$

Short answer

The expression \(5xy - 2x\) is a literal expression, as it contains variables and constants but no final numeric resolution.

Step-by-step solution

Definition of Literal Expression

Understand that a literal expression is an algebraic expression that consists of letters that symbolize numbers, constants, and the arithmetic operations performed on them. It does not contain an actual number resolution and is made up of variables and constants.

Identify Literal Expressions

Examine the given expression, \(5xy - 2x\), to determine if it satisfies the criteria for a literal expression. We identify that the expression consists of variables \(x\) and \(y\), coefficients 5 and -2, and the arithmetic operation of subtraction.

Conclude the Result

Since the expression \(5xy - 2x\) is comprised of variable terms and arithmetic operations but does not resolve to a numerical answer, it is indeed a literal expression.

Key concepts

Algebraic Expressions

Imagine that you are dealing with a mathematical recipe, combining various ingredients like numbers, variables, and operations to create something we call an algebraic expression. An algebraic expression is a collection of constants, variables, and arithmetic operations arranged in a meaningful way to represent a particular mathematical relationship or rule.

These expressions can take many forms, from the simple, like a single variable 'y', to the much more complex, such as quadratic expressions like \(ax^2 + bx + c\). In the example \(5xy - 2x\), the expression is composed of terms that are products of constants and variables. The expression itself stands as an unsolved equation, waiting for values to be substituted into the variables to give a concrete numerical outcome.

These expressions are fundamental to algebra as they are the building blocks for forming equations, which are the puzzles we solve to find the unknown values. As we saw in our exercise, recognizing and handling algebraic expressions is an essential skill in mastering algebra.

Variables in Algebra

In algebra, the use of variables is like adding characters to a story; they represent unknown quantities and play a central role in forming algebraic expressions. Variables are typically denoted by letters such as \(x\), \(y\), or \(z\), and they can take on various values. When solving an algebraic expression or an equation, finding the value of the variable is often our main goal.

Let's consider the expression from our exercise again: \(5xy - 2x\). Here, \(x\) and \(y\) are variables. They symbolize potential numbers and give flexibility to the expression. Through substitution, if we know the value of \(x\) or \(y\), we can calculate the overall value of the expression. This is an indispensable aspect of algebra, enabling us to generalize problems and solve them for a range of values rather than a single set of specifics.

Arithmetic Operations

Arithmetic operations are the actions that tell us what to do with the numbers and variables in an expression. In algebra, we primarily deal with four basic operations: addition, subtraction, multiplication, and division.

In the context of our exercise's expression \(5xy - 2x\), we encounter multiplication and subtraction. Basic arithmetic tells us how to combine these numbers:

• Multiplication (\(5xy\)) signifies that the number 5 (coefficient) is being multiplied by two variables, producing a product.
• Subtraction (the '-' in \(5xy - 2x\)) denotes taking away the value of one term from another.

These operations do more than just calculate; they provide structure and meaning to expressions, defining the relationship between terms. Mastery over arithmetic operations is not just about processing numbers—it's about understanding the syntax of mathematical language and using it to express complex relationships in an easily understood form, which is exactly what algebra is about.