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Chapter 2: Problem 69

Write each phrase as an algebraic expression. \(-14\) added to \(y\)

Short Answer

Expert verified
The algebraic expression is \(y - 14\).

Step by step solution

01

Identify the Components of the Phrase

The phrase consists of two parts: 1. The number \(-14\)2. The variable \(y\)
02

Understand the Operation

The word 'added to' indicates that we need to perform addition.
03

Write the Algebraic Expression

Combine the number \(-14\) and the variable \(y\) using the addition operation. The expression should be \(y + (-14)\).
04

Simplify the Expression (if necessary)

Since adding a negative number is the same as subtracting the number, the expression simplifies to \(y - 14\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Variables
In algebra, a variable is a symbol, often a letter, that stands for a number we do not know yet. The letter can represent any number, making it a flexible tool for solving various problems. In the given exercise, the variable is represented by the letter \( y \). This means that \( y \) can be any number, allowing us to create a general solution. Variables help us to generalize mathematical statements and find solutions that work for a range of values. They are fundamental components in creating and simplifying algebraic expressions.
Performing the Addition Operation
The addition operation is one of the basic arithmetic operations. It combines two numbers or terms to get their total. In our case, the phrase says that \(-14\) is 'added to' \( y \). Here are the steps you need to follow: \
    \
  • Identify the terms to be added. In this exercise, those terms are \(-14\) and \( y \).
    • \
  • Understand that 'added to' signals an addition operation.
    • \
  • Combine the terms using the plus sign: \( y + (-14) \).
    • \
Remember that adding a negative number is the same as subtracting its positive counterpart. So, \( y + (-14) \) simplifies to \( y - 14 \).
Simplification of Algebraic Expressions
Simplifying an algebraic expression means reducing it to its most concise form. This makes the expression easier to understand and work with. In our current exercise, the expression \( y + (-14) \) can be simplified further. Since adding a negative number is equal to subtraction, the expression becomes \( y - 14 \). Here鈥檚 a quick guide on simplification: \
    \
  • Combine like terms, if possible.
    • \
  • Replace addition of negative numbers with subtraction for clarity.
    • \
  • Ensure the expression is as concise as possible without changing its value.
    • \
Simplification helps in solving equations faster and reduces the likelihood of errors.

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