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Chapter 1: Problem 89

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

Short Answer

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

Step by step solution

01

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 \( x \).
02

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 \(-20 - x\).
03

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 \( x \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Subtract. \(4.3-(-0.87)\)

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If \(p\) is a positive number and \(n\) is a negative number, determine whether each statement is true or false. Explain your answer. $$ n-p \text { is always a negative number. } $$

Write any expression, using 3 or more numbers, that simplifies to -11.
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