Problem 37 - Elementary and Intermediate Algebra

Question

Translate to an algebraic expression. 6 increased by \(q\)

Step-by-Step Solution

Answer

6 + q

Step 1: Understand the Problem

The phrase '6 increased by q' means that 6 is added to the variable q. Understanding terms like 'increased by' will help in identifying the right algebraic operation.

Step 2: Identify the Variables and Constants

In this problem, 6 is a constant number and q is a variable.

Step 3: Determine the Operation

The term 'increased by' suggests addition. Thus, the operation involved here is addition.

Step 4: Write the Algebraic Expression

Combine the constant and the variable using the addition operation. The algebraic expression is: 6 + q

Key Concepts

Addition in Algebra

In algebra, understanding how to perform addition with variables and constants is essential. This process is just like arithmetic addition, but it includes letters that represent numbers.

When we talk about addition in algebra, we're often combining numbers (constants) and letters (variables). For instance, in the expression `6 + q`, the `6` is a constant, and `q` is a variable. Here, the `+` symbol tells us to add the two together.

Some key points to remember:

• Addition is commutative: This means that `a + b` is the same as `b + a`.
• When adding constants to variables, just write them side by side: `6 + q`.
• Understand common phrases: 'increased by', 'added to', 'plus' all indicate addition.

Remember these points to simplify your understanding of how addition works in algebra.

Variables and Constants

In algebra, we frequently use variables and constants. Knowing their differences and roles is fundamental.

**Variables**:

• Represent unknown values.
• Can change or vary.
• Usually represented by letters (e.g., `x`, `y`, `q`).

**Constants**:

• Are fixed values.
• Do not change.
• Typically are numbers (e.g., `2`, `3`, `6`).

In the expression `6 + q`:

• `6` is a constant; its value is fixed.
• `q` is a variable; its value can change depending on the problem context.

Understanding these helps in forming and solving algebraic expressions correctly.

Translating Phrases to Expressions

One of the key skills in algebra is translating verbal phrases into algebraic expressions. It allows us to solve real-world problems mathematically.

Let's break down the phrase '6 increased by q':

• '6' is the number we start with.
• 'increased by' indicates addition.
• 'q' is the variable we add to 6.

Putting it all together, we get the expression `6 + q`.

When translating phrases to expressions, focus on these steps:

• Identify the constants and variables.
• Determine the operation (addition, subtraction, etc.) from the keywords.
• Combine them into a single expression.

These steps make it easier to create accurate algebraic expressions from verbal descriptions.