Problem 14 - Elementary Algebra Within Reach

Question

In Exercises \(11-22\), translate the verbal phrase into an algebraic expression. $$ k \text { decreased by } 7 $$

Step-by-Step Solution

Answer

k - 7

Step 1: Analyze the problem

Identify the type of problem and the appropriate mathematical technique to apply.

Step 2: Apply the technique and solve

Apply the identified mathematical method to obtain the solution.

Step 3: Verify the result

Check the answer by substitution or alternative methods to confirm correctness.

Key Concepts

translation of verbal phrases

When working with algebra, translating verbal phrases into algebraic expressions is a foundational skill. This involves interpreting the words and transforming them into mathematical symbols and operations.
For example, the phrase "decreased by" typically indicates subtraction. So, if you have the verbal phrase "k decreased by 7," it means you are starting with a quantity (k) and then reducing it by 7. Therefore, this translates to the algebraic expression: \( k - 7 \).

• Keywords such as "sum," "product," "difference," and "quotient" indicate different operations.
• "Sum" means addition, "difference" means subtraction, "product" means multiplication, and "quotient" means division.

Understanding these translations helps in breaking down complex problems into manageable parts, making them easier to solve.

basic algebra

Basic algebra lays the groundwork for developing mathematical proficiency. It involves understanding how to work with unknowns, often represented by letters like \( k \).
In algebra, letters are used as placeholders for numbers that aren't yet known. For example, in the expression \( k - 7 \), \( k \) represents an unknown value that will be decreased by 7. This kind of setup is typical when expressing relationships or conditions in algebra.

• Algebra uses symbols and letters to create equations and expressions.
• Relying on patterns and structures helps simplify and solve problems.

Basic algebra is about setting up equations and solving them logically to find the unknown values.

algebra for beginners

Algebra can seem challenging at first, but it is approachable with practice and understanding of key concepts. For beginners, it is essential to familiarize oneself with the basic language of math.
Start by recognizing common terminology and formats in algebra. For instance, learning that words like "increased by," "decreased by," "more than," or "less than" correspond to specific operations.

• Practice is crucial: try converting simple verbal phrases into algebraic expressions often.
• Understanding real-world applications can make the subject more relatable and less intimidating.

Also, using tools like visual aids or interactive exercises can help clarify and enforce these beginner concepts, making algebra both comprehensible and enjoyable.