Problem 70 - Algebra 1: Concepts and Skills

Question

Evaluate the expression for the given value of the variable. \(25-n\) when \(n=3\)

Step-by-Step Solution

Answer

The value of the expression when \(n=3\) is 22.

Step 1: Understand the problem

The expression given is \(25 - n\). It needs to be evaluated when the value of \(n\) is 3.

Step 2: Substitute the given value

Substitute \(n = 3\) in the expression \(25 - n\). So the expression becomes \(25 - 3\).

Step 3: Evaluate the expression

Subtract 3 from 25 to get the result. The answer will be \(25 - 3 = 22\).

Key Concepts

Understanding Algebraic Expressions

An algebraic expression is a combination of numbers, variables, and operations. These expressions represent quantities and relationships in mathematics. They are fundamental to understanding equations and functions. Here, the expression is \(25 - n\). The number 25 and the variable \(n\) are combined using the subtraction operation. A few key points to remember about algebraic expressions:

• The numbers (known as constants) do not change.
• The variables (like \(n\) in this case) can represent different values.
• Operations such as addition, subtraction, multiplication, and division connect the numbers and variables.

When dealing with algebraic expressions, it's crucial to understand how these components interact to affect the expression's value.
So in practical terms, if \(n\) changes, the expression's value will change as well.

Substitution in Algebra

Substitution is the process of replacing a variable in an expression with a given value. This is a crucial skill in algebra since it allows for the evaluation of expressions. For the expression \(25 - n\), where \(n = 3\), you substitute the 3 in place of \(n\). Here’s how substitution works:

• Identify the variable in the expression that needs replacing.
• Replace the variable with the given number without altering the operation signs.
• After substitution, the expression \(25 - n\) becomes \(25 - 3\).

Once substitution occurs, you are left with a numerical expression that can be easily evaluated using arithmetic operations. This process transforms an abstract expression into a concrete numerical problem, making it easier to solve.

Performing Basic Arithmetic Operations

Basic arithmetic operations refer to the fundamental operations of addition, subtraction, multiplication, and division. These operations are essential when solving algebraic expressions. For the expression \(25 - 3\), subtraction is the operation used.Here's a simple guide to executing arithmetic operations:

• Identify the numbers and operation involved.
• Perform the operation: Subtraction involves determining how much one number is less than another.
• In this exercise, you subtract 3 from 25 to find the result.
• The final result of the expression \(25 - 3\) is 22.

Subtraction is just one of the basic operations you’ll encounter; each serves a specific purpose in solving different types of mathematical problems. Understanding these concepts of basic arithmetic operations is vital as they form the foundation for more complex math concepts.