Problem 75 - Beginning and Intermediate Algebra

Question

Write each phrase as an algebraic expression. Let \(x\) represent the unknown number. Fifteen more than a number

Step-by-Step Solution

Answer

The expression is \(x + 15\).

Step 1: Identify the Unknown Variable

The problem asks us to express a phrase algebraically, where the unknown quantity is represented by a variable. We will use \(x\) as the variable for the unknown number, as stated.

Step 2: Interpret the Phrase

The phrase 'fifteen more than a number' indicates addition. Specifically, it tells us to add 15 to the unknown number \(x\). This is because 'more than' typically signifies an addition operation in mathematics.

Step 3: Write the Algebraic Expression

Based on the interpretation, we translate 'fifteen more than a number' into the algebraic expression \(x + 15\). This expression represents the sum of the unknown number \(x\) and 15.

Key Concepts

Unknown Variable

In the world of algebra, an unknown variable serves as the placeholder for an uncertain or unspecified number. It allows us to represent expressions and equations in a flexible way so they can be adapted to different scenarios. Typically, letters like \(x\), \(y\), or \(z\) stand in for these unknown variables. In our specific example, we use \(x\) to represent the unknown number. This is a crucial first step in transforming words into algebraic expressions. By choosing a variable, we essentially assign numerical value flexibility to these statements.

• Variables act as symbols for numbers we don’t know yet.
• They are crucial for creating expressions and equations.
• Assigning a variable is usually the first step in algebra problems.

Understanding variables is critical, as they form the backbone of algebraic expressions. The clearer you are with assigning and interpreting variables, the smoother your calculations will become.

Addition in Algebra

The concept of addition in algebra goes beyond simple arithmetic operations. It involves interpreting words like "more than," "sum," or "increased by" as signals for the addition operation. In this exercise, the phrase "fifteen more than a number" directly translates to the operation of adding 15 to our unknown variable \(x\). Recognizing these keywords is pivotal for transforming verbal statements into mathematical expressions.

• "More than" usually means addition is involved.
• Adding 15 to \(x\) forms the expression \(x + 15\).
• Addition operations can change the magnitude of the unknown variable.

Understanding these terms in the context of algebra helps in correctly interpreting and forming expressions. The mastery of these translations is essential as you progress in solving more complex problems.

Mathematical Interpretation

Mathematical interpretation is the process of translating verbal instructions into mathematical expressions or problems. It plays a critical role in understanding exercises and solving them correctly. As we encountered in the step by step solution, interpreting "fifteen more than a number" involved understanding the phrase as a directive for addition. This interpretive step is crucial as it directly impacts how you set up the algebraic expression, like our \(x + 15\) in this scenario.

• It requires analyzing and converting words into symbols.
• Good interpretation skills lead to accurate formulations.
• Practicing different problem statements helps refine these skills.

Effective mathematical interpretation provides a solid foundation for working not only with basic algebraic expressions but also with more intricate formulas and equations in advanced topics.