Problem 16 - Algebra 1

Question

Write the verbal phrase as an algebraic expression. Use \(x\) for the variable in your expression. A number increased by seven

Step-by-Step Solution

Answer

The algebraic expression for the phrase 'A number increased by seven' is \(x + 7\).

Step 1: Identify the Variable

'A number' in the phrase denotes a variable. According to the instructions, this variable is represented as \(x\).

Step 2: Translate 'Increased by Seven'

The phrase 'increased by seven' implies the operation of addition with the number 7. In algebra, this is written as \(+ 7\).

Step 3: Formulate the Expression

Combining the variable \(x\) with the operation \(+ 7\) gives the algebraic expression \(x + 7\).

Key Concepts

Understanding Variables in Algebra

Variables are fundamental elements in algebra, often represented by letters such as \(x\). They act as placeholders for numbers whose values are not yet known or can change. In a problem like "a number increased by seven," the phrase "a number" indicates a variable. Using variables in expressions allows us to generalize mathematical statements, making them applicable in numerous situations.

• Variables can represent any number.
• They help formulate general rules and patterns in mathematics.

Choosing a letter like \(x\) to represent a variable in an expression is common in algebra. It's a flexible choice that allows for concise mathematical communication.

Addition in Algebraic Expressions

Addition is one of the core operations in mathematics, symbolized by the plus sign \(+\). When constructing algebraic expressions, addition is used to denote the combining of values. In the expression "a number increased by seven," the term "increased by" instructs you to perform addition on the variable by 7.

• Addition helps in determining total amounts or combining quantities.
• In algebra, placing a number after the \(+\) sign suggests that number is being added to the variable.

For instance, if the variable \(x\) is chosen to represent "a number," then the expression becomes \(x + 7\). This symbolic notation explicitly shows the operation and the values involved.

Translating Word Problems into Algebraic Expressions

Translating word problems into algebraic expressions involves converting phrases and statements into mathematical language. This skill is essential in finding solutions to real-world problems. Start by identifying keywords and recognizing the operations they imply. In the phrase "a number increased by seven,"

• "A number" translates to a variable like \(x\).
• "Increased by" translates to the addition operation, represented by \(+\).
• "Seven" remains as the number 7 in the expression.

Combining these elements results in the algebraic expression \(x + 7\). Practicing these translations can improve understanding and ease in solving more complex problems in algebra.