Problem 22 - Algebra 1

Question

Write the verbal phrase as an algebraic expression. Use \(x\) for the variable in your expression. Twenty-nine decreased by a number

Step-by-Step Solution

Answer

The algebraic expression for the verbal phrase 'Twenty-nine decreased by a number' is \(29 - x\).

Step 1: Identify the components

Firstly, identify the parts of the sentence that refer to numbers or operations. 'Twenty-nine' is a number and 'decreased by' implies a subtraction operation.

Step 2: Formulate the expression

In light of the operation identified in Step 1, translate the phrase into an algebraic expression using the variable \(x\). 'Twenty-nine decreased by a number' translates to \(29 - x\).

Key Concepts

Subtraction in Algebra

In algebra, subtraction is a fundamental operation that involves taking one quantity away from another. The key to understanding subtraction in algebra is recognizing the implication of phrases like "decreased by" as instructions to subtract.
When performing subtraction in algebra, make sure to:

• Identify the minuend, which is the initial number or expression from which another quantity is subtracted.
• Recognize the subtrahend as the number or variable being subtracted from the minuend.
• Retain the order since subtraction is not commutative. For example, in the expression \(29 - x\), \(29\) is the minuend and \(x\) is the subtrahend, not the other way around.

Remember, subtraction reduces the value of the initial number or expression by the value of the subtracted term.

Translating Verbal Phrases

Translating verbal phrases into algebraic expressions is a skill that improves with practice. The goal is to convert a written phrase into a mathematical form using symbols and variables. For example, in the phrase "twenty-nine decreased by a number," each word relates to an algebraic symbol or operation.

• "Twenty-nine" suggests the number \(29\).
• "Decreased by" indicates the subtraction operation.
• "A number" implies an unknown variable, often represented as \(x\) in algebra.

Translating verbal phrases often involves recognizing keywords that dictate mathematical operations. Words like "sum," "plus," or "increased by" denote addition, while "difference," "less," or "decreased by" relate to subtraction. Successful translation allows the expression \(29 - x\) to accurately represent the phrase.

Variables in Expressions

Variables are symbols, typically letters, used to represent unspecified numbers in expressions and equations. In algebraic expressions, these variables allow for the generalization of mathematics to represent relationships and solve problems in different scenarios.
When incorporating variables like \(x\):

• Understand that \(x\) can take on any value, making the expression versatile for multiple situations.
• Variables serve as placeholders that can change, enabling solutions for equations where specific values provide true statements.
• Recognize them as essential in constructing expressions like \(29 - x\), which indicates that twenty-nine is adjusted by any value \(x\) can assume.

This flexibility makes variables powerful tools for creating models and solving for unknowns in various mathematical contexts.