Problem 31 - Introductory Algebra for College Students

Question

Write each English phrase as an algebraic expression. Let the variable \(x\) represent the number. nine subtracted from a number

Step-by-Step Solution

Answer

The algebraic expression for 'nine subtracted from a number' is \(x - 9\).

Step 1: Identify the operation

The problem is asking to subtract nine from a number. The key word here is 'subtracted', which indicates the operation to use.

Step 2: Identify the number involved

The problem mentions that the number from which nine is to be subtracted is a variable, \(x\). This is what we are subtracting from.

Step 3: Formulate the expression

Knowing that we are subtracting nine from a number \(x\), the expression will be \(x - 9\).

Key Concepts

Understanding Variables

In algebra, a **variable** is a symbol, typically a letter, that represents a number we don’t yet know. It's like a placeholder in expressions or equations, standing in for the unknown value. For example, the variable \( x \) can represent any number, and it’s used to form expressions and solve equations. Here are a few key points about variables:

• Variables allow us to write general rules and formulas.
• They are essential for translating real-world problems into mathematical language.
• In the example given, \( x \) is the variable representing 'a number' we are working with.

Understanding variables is crucial in algebra because they form the backbone of expressions and equations. **Mastering the use of variables helps you solve problems where the exact number isn’t immediately known.**

The Role of Subtraction in Algebra

**Subtraction** is one of the basic arithmetic operations used frequently in algebra. It involves taking one number away from another. In the context of algebraic expressions, understanding subtraction helps you manipulate and solve them effectively.In our example, the phrase 'nine subtracted from a number' translates into subtracting 9 from the variable \( x \). Here's how subtraction functions in this context:

• The order matters: Subtracting \(9\) from \(x\) means \(x - 9\), not \(9 - x\).
• Subtraction can be combined with other operations to form complex expressions.
• It's crucial for solving equations and finding unknown values.

By mastering subtraction, you're able to simplify expressions and make sense of algebraic terms more easily, paving the way for solving a variety of mathematical problems.

Translating Word Problems to Algebraic Expressions

One of the most important skills in algebra is **translating word problems into algebraic expressions**. This involves converting a descriptive problem or statement into an equation or expression that can be solved using algebra.Here is a step-by-step approach:

• Identify key numbers and operations mentioned in the problem.
• Use a suitable variable to represent unknown quantities.
• Write down the expression using correct mathematical symbols for operations.

In the problem "nine subtracted from a number," these steps were applied as follows:- **Identify operation**: Recognize that "subtracted" means you'll use subtraction.- **Choose the variable**: Use \( x \) to represent "a number."- **Form the expression**: Translate "nine subtracted from a number" to \( x - 9 \).Mastering this skill helps in solving more complex algebra problems, by enabling you to convert real-world situations into a clear and solvable form. This ability makes algebra a powerful tool for understanding and solving everyday challenges.