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Chapter 1: Problem 47

Write each word phrase as an algebraic expression, using \(x\) as the variable. The difference between a number and 8

Short Answer

Expert verified
x - 8

Step by step solution

01

Identify the Key Components

The phrase 'the difference between a number and 8' indicates that you need to subtract 8 from a number. Here, the 'number' refers to the variable, which is denoted as 'x'.
02

Translate the Phrase to Math

To represent this phrase algebraically, we need to express it as the difference of x and 8. This is done by subtracting 8 from x.
03

Write the Algebraic Expression

Putting it all together, the algebraic expression that represents the phrase 'the difference between a number and 8' is: \[ x - 8 \]

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Key Concepts

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

Translation of Word Phrases
In mathematics, translating word phrases into algebraic expressions is a common task. It helps to convert everyday language into mathematical language, making problem solving easier. The phrase 'the difference between a number and 8' is an example.
To start, identify key words:
  • 'Difference' suggests subtraction.
  • 'A number' indicates a variable, often represented by x.
  • 'And 8' tells us 8 is the number being subtracted.
Using these hints, we can create the algebraic expression by understanding what each part represents and converting it step-by-step.
Basic Algebra
Basic algebra involves using letters, or variables, to represent numbers. This allows us to create general formulas that work across different situations. For instance, if we say 'a number' and use x as our variable, x stands in for any number.
Here鈥檚 the breakdown:
  • Recognize phrases such as 'a number' as variables.
  • Understand operations like 'difference' as mathematical operations (e.g., subtraction).
Having this foundational understanding is crucial. It bridges the gap between word problems and algebraic expressions, making it easier to solve.
Variable Subtraction
When dealing with variable subtraction, such as 'the difference between a number and 8', you follow logical steps. Variable subtraction simply means we are subtracting a number from a variable.
The steps are quite straightforward:
  • Identify the variable (e.g., x).
  • Determine what number is being subtracted (e.g., 8).
  • Write it out as an expression (e.g., x - 8).
This makes it convenient to work with different values for the variable x as needed.

Through these steps, you can transform descriptive phrases into workable algebraic expressions. This is fundamental for solving more complex algebra problems.

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Most popular questions from this chapter

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. \(23,18,13,-4,\) and \(-8\)

Solve each problem. Two sockets in a socket wrench set have measures of \(\frac{9}{16}\) in. and \(\frac{3}{8}\) in. What is the difference between these two measures?

Select the lesser of the two given numbers. \(-16,-17\)

Use the commutative or the associative property to complete each statement. State which property is used. See Examples I and 2. $$ 8 \cdot(6 \cdot 4)=(8 \cdot \quad) \cdot 4 $$

Write each word statement as an equation. Use \(x\) as the variable. Find all solutions from the set \(\\{2,4,6,8,10\\} .\) See Example 5 The sum of a number and 8 is \(18 .\)
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