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Chapter 3: Problem 78

Write each phrase as a variable expression. Use \(x\) to represent "a number." Twice a number

Short Answer

Expert verified
The expression is \(2x\).

Step by step solution

01

Identify Keywords

The phrase 'Twice a number' indicates the mathematical operation of multiplication of a number by 2. Here, 'Twice' refers to multiplying by 2, and 'a number' is represented by the variable \(x\).
02

Write the Expression

Based on the identified keywords in Step 1, write the expression using the variable \(x\). Since 'Twice' means multiplying by 2, the expression is: \(2x\).
03

Verify the Expression

Check if the mathematical expression \(2x\) correctly represents 'Twice a number'. Each part of the phrase has been translated correctly: 'Twice' corresponds to the factor of 2, and 'a number' is denoted by \(x\).

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Key Concepts

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

Understanding Variable Expressions
Variable expressions are a fundamental part of algebra. They allow us to describe mathematical phrases using variables, which are symbols that stand for unknown numbers or values. For instance, consider the phrase "a number." Instead of a specific number, we can use a variable like \(x\) to represent this idea. This gives us a lot of flexibility in equations and allows for the creation of general solutions or rules.
Here are some key points to remember:
  • A variable is a placeholder for an unknown value.
  • Variable expressions can include numbers, operations, and variables.
  • They are used to model real-world situations mathematically.
By "writing a phrase as a variable expression," we translate words into algebraic terms, helping to make the problem more manageable and systematic.
Basics of Multiplication with Variables
Multiplication involving variables is a key aspect of forming algebraic expressions. When you see a phrase like 'Twice a number,' it means multiplying a given number by two. In algebra, we use a variable such as \(x\) to stand for 'a number.' Therefore, 'Twice a number' translates into \(2x\).
Here are some helpful reminders when working with multiplication and variables:
  • The number in front of the variable, like 2 in \(2x\), is called the coefficient. It tells you how many times to multiply the variable.
  • "Twice" means multiplying by 2; similarly, "three times" would mean multiplying by 3, and so on.
  • Variable expressions are often simplified by combining like terms if possible.
This approach of using multiplication helps to simplify larger expressions and solve equations efficiently.
Crafting Algebraic Expressions
Algebraic expressions like \(2x\) are built using numbers, variables, and operations. These expressions allow us to solve problems where we might not know all the values upfront but can express relationships and perform operations with those unknowns.
To understand and create algebraic expressions:
  • Start by identifying what the variable represents, in this case "a number," signified by \(x\).
  • Consider what operations are indicated by the words, "Twice" implies multiplication.
  • Combine the numbers and variables to build the expression: \(2x\) stands for 'Twice a number.'
Algebraic expressions are the backbone of many mathematical problem-solving strategies. They help us create equations that model and solve real-world problems effectively.

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Most popular questions from this chapter

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