Problem 89 - Algebra A Combined Function

Question

Translate each phrase to an algebraic expression. Use " \(x\) " to represent "a number." Subtract a number from -20 .

Step-by-Step Solution

Answer

The expression is \(-20 - x\).

Step 1: Identify the Key Components

The key phrase here is 'subtract a number from -20.' This means we need an operation where we start with -20 and remove or take away a number from it. The number in question is not specified, so we represent it with the variable \( x \).

Step 2: Set Up the Expression

In mathematical terms, the phrase 'subtract a number from' translates to using the subtraction operator (\(-\)). The expression starts with -20, from which we subtract \( x \). This gives us the algebraic expression \(-20 - x\).

Step 3: Verify the Expression

Check that the expression accurately represents the phrase. The phrase calls for a number being subtracted from -20, and the expression \(-20 - x\) correctly captures this relationship, where we start with -20 and subtract \( x \).

Key Concepts

Translating Phrases to Expressions

Translating phrases into algebraic expressions is a crucial skill in algebra. It enables us to convert real-world problems or verbal statements into mathematical models that we can analyze and solve. When you see a phrase like "subtract a number from -20," it's essential to break it down into components that can be expressed mathematically.

• The phrase "a number" refers to an unknown quantity, which we usually represent with a variable, like \( x \).
• The word "subtract" indicates that we need to perform a subtraction operation.
• The phrase "from -20" tells us our starting point, which is the number -20.

By understanding each part of the phrase, we translate it to the expression \(-20 - x\). This process allows us to effectively work with complex problems by breaking them down into simpler parts.

Using Variables in Expressions

Variables are a fundamental aspect of algebra. They stand in place of numbers that either are unknown or can change. For the phrase "subtract a number from -20," \( x \) is used as the variable to represent "a number." This is because the specific number is not given in the problem.When you use variables in expressions, they add flexibility and generality:

• Variables allow you to express general principles that apply to many different cases, rather than a single numerical situation.
• Using a variable like \( x \), you can easily update the expression when you know more about the specific value.

Remember, a variable can represent any number, and in algebra, it helps link abstract concepts to concrete operations, like subtraction in this exercise.

Subtraction in Algebra

Subtraction is a fundamental operation in math, and it's equally critical when dealing with algebraic expressions. In the given exercise, the operation you perform is subtraction, specifically indicated by the word "subtract."

• When you subtract a variable (\( x \)) from a number (like -20), it changes the value or decreases the starting number.
• The expression \(-20 - x\) shows that \( x \) is taken away from -20. This matches the phrase "subtract a number from -20."

Understanding how subtraction works in algebra is key. It involves not just taking away a number but also accurately reflecting this operation in an expression. Here, it's important to start with the number you're subtracting from (in this case, -20) and then subtract the variable \( x \). This approach helps clear up any confusion about the order of operations and ensures you're performing the right computation.