Problem 20 - Algebra 1

Question

Write the verbal phrase as an algebraic expression. Use \(x\) for the variable in your expression. Difference of ten and a number

Step-by-Step Solution

Answer

The algebraic expression for 'Difference of ten and a number' is \(10 - x\).

Step 1: Identify the operations

The key to this kind of problems is to identify the operations suggested by the words used in the phrase. Here, 'difference' suggests subtraction.

Step 2: Identify the numbers

The next step is to identify the numbers involved, which here are 'ten' and 'a number'. 'A number' suggests an unknown, which we can represent with a variable, in this case 'x'.

Step 3: Write the expression

Finally we write an algebraic expression corresponding to the phrase, using the identified operation and numbers. Here, 'Difference of ten and a number' translates to '10 - x'.

Key Concepts

Verbal Phrases in Algebra

In algebra, verbal phrases are words that describe mathematical operations and relationships. They are like sentences that we translate into math expressions. Understanding verbal phrases helps bridge the gap between everyday language and mathematical language.

For example, in the phrase "difference of ten and a number," each part of the sentence holds mathematical significance.

• "Difference" signals that we need to use subtraction.
• "Ten" is a specific number in the problem.
• "A number" symbolizes a quantity that we don’t know.

The task is to convert this phrase into an algebraic expression, representing it using numbers and variables. Mastering this skill is crucial for solving word problems and performing algebraic operations easily.

Variables in Algebra

Variables are essential in algebra as they represent unknown or changeable values. They allow us to create general formulas and expressions that can describe numerous situations. Often depicted by letters like \( x \), \( y \), or \( z \), variables enable flexibility and generalization in mathematical modeling.

In our case, "a number" in the verbal phrase "difference of ten and a number" is represented by the variable \( x \). This means instead of directly knowing what this number is, we use \( x \) to stand in for any number. Variables make it easy to write expressions and solve for unknowns, because they function like placeholders in equations. This concept is foundational in algebra, paving the way for more complex problem-solving techniques.

Subtraction in Algebra

Subtraction is one of the fundamental operations in algebra. It's the process of finding the difference between numbers, which is a common requirement in both simple and complex equations. When dealing with verbal phrases, identifying subtraction is key. Words like "difference," "less," and "minus" often indicate the need for this operation.

In the phrase "difference of ten and a number," subtraction is signified by "difference." We place the known number first, which is ten, and subtract the variable, which is \( x \). Thus, the algebraic expression becomes \( 10 - x \). Understanding subtraction in algebra allows for the interpretation of various operations and scenarios, making it a vital skill in mathematical problem-solving.