Problem 77 - Beginning and Intermediate Algebra

Question

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. Five subtracted from a number

Step-by-Step Solution

Answer

\(x - 5\)

Step 1: Identify the Unknown

Determine the variable that will be used to represent the unknown number in the problem. Here, we let \(x\) represent the unknown number.

Step 2: Understand the Phrase

Break down the phrase 'Five subtracted from a number.' This means you need to take away five from some number, which is represented by \(x\).

Step 3: Write the Algebraic Expression

Translate the phrase 'Five subtracted from a number' into an equation by subtracting 5 from \(x\). This gives the expression: \(x - 5\).

Key Concepts

Unknown Variable

In algebra, an unknown variable acts as a placeholder for an unknown or changing quantity. It is often represented by a letter such as \(x\). In our exercise, the unknown number we need to work with is unknown, so we choose \(x\) to symbolize it.

Choosing a variable is extremely helpful when solving algebraic problems because it simplifies complex phrases and equations.

• The letter used as the variable is arbitrary, meaning you could also use letters like \(y\) or \(z\), but \(x\) is common.
• Variables can represent a range of numbers or specific, unknown values.

With an unknown variable in place, you can transform real-world problems into mathematical expressions, making them easier to solve and analyze.

Phrase Translation

Phrase translation is essential in algebra because it converts words into mathematical expressions. To effectively translate phrases, understanding the meaning of common terms is crucial. Let's break down the exercise phrase: "Five subtracted from a number."

• "Five subtracted from": This indicates a subtraction operation where 5 is being taken away from another value.
• "a number": This represents our unknown variable, \(x\), which we decided earlier.

So, combining these interpretations, the phrase "Five subtracted from a number" mathematically translates to \(x - 5\).

To master phrase translation, practice analyzing various phrases and identifying keywords that indicate operations like addition, subtraction, multiplication, and division.

Subtraction in Algebra

Subtraction in algebra operates much like regular subtraction, but with variables and sometimes multiple terms. It involves removing one quantity from another. In our exercise, we interpret "Five subtracted from a number" as subtracting 5 from the unknown variable \(x\), resulting in \(x - 5\).

Here are key points to remember about subtraction in algebra:

• The order of terms matters: For example, \(5 - x\) is different from \(x - 5\) because the former subtracts \(x\) from 5, while the latter subtracts 5 from \(x\).
• Subtraction can be used in conjunction with both known numbers and other variables.
• Sometimes, subtraction is part of a larger equation that involves combining like terms or simplifying expressions.

Understanding subtraction and its notation in algebra will help you accurately solve and simplify various algebraic problems.