Problem 18 - Algebra 1: Concepts and Skills

Question

Write the phrase as a variable expression. Let x represent the number. 6 less than a number

Step-by-Step Solution

Answer

\(x - 6\)

Step 1: Understanding the phrase

The phrase '6 less than a number' means we are subtracting 6 from a certain number. Here, our number is represented by x.

Step 2: Writing the expression

In mathematical terms, when we say '6 less than a number', we mean the number (x) minus 6. So we write this as \(x - 6\).

Key Concepts

Algebraic Expressions

Algebraic expressions are like sentences in math. They use numbers, variables, and operators (like addition or subtraction) to convey a mathematical idea. In our exercise, we have the phrase "6 less than a number."

This is turned into an algebraic expression by representing "a number" as a variable, commonly written as \(x\). The variable \(x\) acts like a placeholder for any number we don't yet know. So, when we construct the expression, we simply follow the instruction in the phrase using the variable and numbers: \(x - 6\). This new expression \(x - 6\) means you're subtracting 6 from the unknown number \(x\).

Algebraic expressions are essential because they help us set up equations to solve puzzles involving unknown numbers. They're like blueprints for figuring things out mathematically.

Mathematical Phrases

Mathematical phrases are the language tools we use to describe mathematical operations in everyday language. They often contain words that translate into specific arithmetic operations. Let's break down the phrase "6 less than a number," as seen in the exercise.

First, identify the key components:

• "6" - This is a number we will use in the calculation.
• "less than" - This phrase indicates subtraction, telling us to remove 6 from something else.
• "a number" - This is the unknown quantity, which we call \(x\).

By understanding each part, we can rewrite it as the algebraic expression \(x - 6\). This skill is valuable because it allows us to convert words into formulas, helping us apply math to real-world problems.

Subtraction in Algebra

Subtraction in algebra works similarly to subtraction with regular numbers, but because we often work with variables, it can sometimes feel a bit more abstract.

When you see a phrase like "6 less than a number," it's explaining that you'll be taking 6 away from an unknown value \(x\). This type of expression, \(x - 6\), is straightforward once you get the hang of it. The subtraction operation here takes place between the variable \(x\) and the number 6.

Subtraction is one of the core arithmetic operations and is important for solving equations. In algebra, you often move terms to either side of an equation using addition or subtraction. It's all about balancing the scales by understanding and applying the rules of arithmetic effectively.