Problem 91 - Algebra 1

Question

Find the terms of the expression. $$31-15 n$$

Step-by-Step Solution

Answer

The terms of the expression are '31' and '-15n'.

Step 1: Identify the Terms

In the algebraic expression '31 - 15n', there are two terms.

Step 2: First Term

The first term is '31'. This is a constant term because it does not contain a variable.

Step 3: Second Term

The second term is '-15n'. This term is a variable term as it contains both a number (-15) and a variable (n). The negative sign is part of this term.

Key Concepts

Constant Term

In algebra, a constant term is a number that does not change its value. It stands alone without any variables attached to it, which means that no matter what value you substitute for any variables in the equation or expression, the constant term remains the same. In the provided exercise with the expression 31 - 15n, the number '31' is identified as the constant term. It's a fixed number and does not vary with 'n', the variable in the expression.

Understanding constant terms is essential because they help us to evaluate expressions when values for the variables are known. In an equation, constant terms can shift to the opposite side of the equation to isolate the variable for solving purposes, a fundamental step in simplification and solvation processes of algebra.

Variable Term

The term variable term refers to a component of an algebraic expression that includes both a number and a variable. The number part is sometimes called a coefficient, which multiplies the variable. For example, in the term '-15n' from the expression 31 - 15n, '-15' is the coefficient, and 'n' is the variable. It's important to note that the negative sign is considered a part of the term, indicating the direction of its effect in an equation or expression.

Variable terms will change their value depending on what you substitute for the variable. The significance of recognizing a variable term lies in the fact that it allows algebraic expressions to represent patterns and relationships between quantities that can vary, making it an essential concept in constructing equations and modeling real-world scenarios.

Algebraic Expression

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like 'n'), and operations (such as addition and subtraction). For instance, 31 - 15n is an algebraic expression composed of a constant term '31', and a variable term '-15n'. The expression represents a specific numerical value once the variable has been assigned a value.

Algebraic expressions are building blocks of algebra and are used to describe mathematical relationships. They provide a convenient way to encapsulate a rule in a mathematical form, which can then be manipulated to solve problems. Understanding how to identify and work with algebraic expressions is fundamental to progressing in mathematics because they are used to solve equations, develop formulas, and model real-life situations mathematically.