Problem 80 - Algebra A Combined Function

Question

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. A number increased by 9

Step-by-Step Solution

Answer

The expression is \(x + 9\).

Step 1: Understand the Phrase

The phrase "a number increased by 9" means you start with a number and add 9 to it. We are told that the number is represented by the variable \(x\).

Step 2: Identify the Operation

Since the phrase mentions "increased by," it implies an addition operation. Thus, you should add 9 to the number \(x\).

Step 3: Formulate the Expression

Combine the number \(x\) with the number 9 using the addition operation. This results in the algebraic expression \(x + 9\).

Key Concepts

Addition Operation

When you see the phrase "increased by," it usually indicates an addition operation in algebraic expressions. The addition operation involves combining two numbers or quantities. Here, we have a number represented by the variable \(x\) and the number 9. To "increase" a number is to make it larger by adding a certain value to it.

Addition is denoted by the symbol \(+\). It is used to find the sum of two numbers or quantities. So in our example, by adding 9 to \(x\), we get the expression \(x + 9\). This equation represents a number that has been increased by 9, where \(x\) is the original number.

Addition is a fundamental operation in mathematics and helps to simplify and express more complex equations.

Variables in Algebra

Algebra often uses symbols to stand for numbers. These symbols are called variables. In this exercise, the variable is \(x\). Variables in algebra are like placeholders, they can represent unknown numbers or values.

Using variables makes it easier to write and solve algebraic expressions and equations. Instead of writing "a number," you write \(x\). This allows you to express general rules and relationships between numbers.

• \(x\) could be any number: positive, negative, integer, or even a fraction.
• Variables allow you to solve problems that have solutions that vary.
• They open up more flexibility in problem-solving.

Recognizing and understanding variables is crucial because they are used to manipulate numbers and solve various mathematical problems. This exercise reinforces that connection by expressing a phrase with a variable.

Writing Expressions

Writing expressions is a skill that enables you to transform written phrases into mathematical form. This transformation helps communicate mathematical ideas clearly and concisely. With practice, you can convert any verbal description into an algebraic expression.

Let's look at the phrase "a number increased by 9". By associating the unknown number with the variable \(x\), and "increased by" with the addition operation, we directly write the expression \(x + 9\).

• Identify the numbers or variables mentioned in the phrase.
• Determine the operation indicated by the words.
• Formulate the expression by combining numbers/variables with the operations.

Each component of the phrase becomes an integral part of the expression. Understanding this process ensures that complex sentences can be broken down into smaller, manageable parts that you can translate into algebra.