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Chapter 1: Problem 113

Translate to an algebraic expression.[ 1.1] Nine more than twice a number

Short Answer

Expert verified
2x + 9

Step by step solution

01

Identify the unknown

Identify the variable that represents the unknown number. Let this unknown number be represented by the variable 鈥渪鈥�.
02

Twice the number

Multiply the variable by 2 to represent twice the number. Thus, twice the number is written as 2x.
03

Add nine

Add nine to the expression representing twice the number. This results in the expression 2x + 9.
04

Construct the algebraic expression

Combine all the steps to form the final algebraic expression: 2x + 9.

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Key Concepts

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

Variables in Algebra
In algebra, we use variables to represent unknown values. A variable is usually a letter such as x, y, or z. It acts as a placeholder for a number we do not yet know. Typically, you will encounter these variables in mathematical equations and expressions.

For example, in the expression 2x + 9, 'x' is the variable. It stands in for a number we want to find. Using variables makes it easier to write and solve equations.
To understand variables better, remember:
  • They can be any letter.
  • They represent unknown numbers.
  • They help simplify complex problems.
Understanding how to work with variables is the first step in mastering algebra.
Translating Phrases to Algebra
Translating phrases into algebraic expressions is a key skill in algebra. This involves converting words into mathematical symbols and numbers.

Let's break down the given phrase 'Nine more than twice a number':
鈥� 'A number' means an unknown value, which we'll call x.
鈥� 'Twice a number' means 2 times x, or 2x.
鈥� 'Nine more than' means you add 9 to this value.

So, when we translate the phrase 'Nine more than twice a number' into an algebraic expression, it becomes 2x + 9.
This process of changing words to symbols is important because it allows you to solve real-world problems using algebra.
Basic Algebra Operations
Basic algebra operations involve addition, subtraction, multiplication, and division with variables.

In the expression we translated, 2x + 9 involves two algebraic operations:
  • Multiplication: 2 times x (written as 2x).
  • Addition: Adding 9 to the result (written as 2x + 9).

These operations follow the same rules as basic arithmetic, but now we apply them to variables as well.

Understanding these basic operations is crucial:
  • They form the foundation of more complex equations.
  • They help in performing step-by-step calculations.
Mastering these techniques will make it easier to handle more advanced algebra concepts in the future.

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Most popular questions from this chapter

Perform the indicated operation and, if possible, simplify. If there are no variables, check using a calculator. $$ \frac{x}{5} \cdot \frac{y}{z} $$

Find the prime factorization of each number. If the number is prime, state this. $$ 98 $$

SYNTHESIS Write the sentence \((-x)^{2} \neq-x^{2}\) in words. Explain why \((-x)^{2}\) and \(-x^{2}\) are not equivalent.

Translate to an inequality. The distance from \(t\) to 0 is at least \(20 .\)

List in order from least to greatest. $$\frac{4}{5}, \frac{4}{3}, \frac{4}{8}, \frac{4}{6}, \frac{4}{9}, \frac{4}{2},-\frac{4}{3}$$
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