Problem 75 - Intermediate Algebra

Question

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. Nine less than twice a number

Step-by-Step Solution

Answer

The algebraic expression is \(2n - 9\).

Step 1: Understanding the Phrase

We need to translate the English phrase 'Nine less than twice a number' into an algebraic expression. Here, the unknown number is represented by \(n\).

Step 2: Identifying the Components

The phrase 'twice a number' indicates a multiplication by 2, which results in \(2n\). Next, 'nine less than' means we will subtract 9 from this result.

Step 3: Constructing the Expression

From the identified components, we start with 'twice a number', \(2n\), and then subtract 9 to account for 'nine less than'. So the expression becomes \(2n - 9\).

Key Concepts

Translation of Phrases

Algebra often begins with translating everyday language into mathematical expressions. This process is known as 'translation of phrases'. In our example, the phrase is "Nine less than twice a number". To successfully translate:

• Identify key mathematical terms: "twice", "less than", "a number".
• "Twice" indicates multiplication by 2.
• "Less than" suggests subtraction.

Recognize the phrase "a number" as an indication of an unknown variable. By understanding these terms, you can transform the entire sentence into a math expression. This is why interpreting and translating accurately is important in algebra.

Unknown Variables

In algebra, unknown variables are often represented by letters such as \(n\). These variables stand for numbers we don't yet know. In the phrase "Nine less than twice a number", \(n\) is our unknown variable, representing "a number".

• This allows flexibility in solving equations.
• The goal is often to find the value of this variable.

Using variables helps turn word problems into equations. When writing math expressions, understanding the concept of substitution with variables is key. It allows you to set up and solve algebraic equations easily.

Algebra Problem Solving

Once you've translated a phrase into a math expression, the next step is problem solving. In our case, the expression becomes \(2n - 9\). Here:

• "Twice a number" changes into \(2n\).
• "Nine less than" means subtracting 9, resulting in \(2n - 9\).

By constructing and solving such expressions, you can find specific values for your variables when given additional information.Algebra problem solving often involves performing operations like addition, subtraction, multiplication, or division. Mastering these skills is essential to tackle more complex algebraic problems in the future.