Problem 81 - Algebra A Combined Function

Question

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

Step-by-Step Solution

Answer

The expression is \( x - 5 \).

Step 1: Translate the phrase

"Five subtracted from a number" means we start with the number \(x\) and subtract 5 from it.

Step 2: Write the expression

The algebraic expression is \(x - 5\).

Key Concepts

Subtraction

Subtraction is a fundamental operation in mathematics where you take away one number from another. In simple terms, if you have a number of apples and someone takes some away, subtraction tells you how many apples are left. When writing subtraction mathematically, you use the minus sign "-" to indicate the operation.
Imagine you're working with numbers: if you subtract 5 from 10, it looks like this in mathematics:

• 10 - 5 = 5

This represents taking away 5 from 10, leaving us with 5.
When we perform subtraction in algebra, it works similarly, but we sometimes don't know the exact numbers involved. This is where variables come into play, and subtraction helps us work with these unknowns.

Variables in Algebra

Variables in algebra represent unknown numbers and help us create equations or expressions. Think of variables as placeholders for numbers we don't know yet, symbolized by letters such as \(x\), \(y\), or \(z\).

In the given problem, the variable \(x\) represents an unknown number. Using variables in mathematics allows us to generalize and solve a variety of problems. For instance, if we say "a number plus 3" is \(x + 3\), \(x\) can take any value, and you can find specific results by plugging numbers into \(x\).

Variables make algebra powerful because they give the flexibility to work with equations and expressions even when we don't know every number involved initially.

Translating Phrases into Algebra

Translating phrases into algebra involves converting words into mathematical expressions. This skill helps bridge real-life situations with mathematics, making sense of problems. Consider the phrase "Five subtracted from a number." To express this in algebra:
- Identify the number, which is often unknown—here, represented by \(x\).- Understand the action "subtracted from," which tells us we need to perform subtraction.

To translate, switch the order of the words heard. "Five subtracted from a number" converts to \(x - 5\). Note how this reverses the order compared to how we might say it in English.

• The number (\(x\)) first
• Minus the number to be subtracted (5)

Successfully translating words into algebra makes it easier to solve complex problems and showcases how language transforms into mathematical meaning.