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Chapter 1: Problem 44

Write each word phrase as an algebraic expression, using \(x\) as the variable. Seven subtracted from a number

Short Answer

Expert verified
The algebraic expression is \(x - 7\).

Step by step solution

01

Identify the variable

The phrase mentions 'a number'. Represent this unknown number with the variable, which is given as \(x\).
02

Identify the operation

The phrase specifies 'seven subtracted from a number'. The word 'subtracted' indicates that it is a subtraction operation.
03

Set up the algebraic expression

'Seven subtracted from a number' translates to \(x - 7\).

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Key Concepts

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

writing expressions
Writing expressions in algebra is like creating a short and clear way to represent mathematical ideas. Think of it as translating words into math language. When a phrase like 'seven subtracted from a number' is given, your job is to turn these words into an algebraic expression.

Here's how you do it:
  • First, identify the number or the variable involved. In our case, it鈥檚 a number which we will call x.
  • Next, identify the operation described in the phrase. Here, it's 'subtracted', which means we are dealing with subtraction.
  • Finally, put it all together to form the expression. 'Seven subtracted from a number' becomes x - 7.
Remember, the order of the words matters. 'Seven subtracted from a number' is different from 'a number subtracted from seven', which would translate to 7 - x. Always pay close attention to the words to set up your expressions correctly.
subtraction in algebra
Subtraction in algebra can sometimes be tricky, especially when it comes to word problems. It鈥檚 all about understanding the order in which numbers or variables should be placed.

For example:
  • 'Seven subtracted from a number' means that you take a number (x) and you subtract 7 from it. This is written as x - 7.
  • In subtraction, the order is crucial. If the phrase was 'a number subtracted from seven', the expression would change to 7 - x.
Another important point is that subtraction is not commutative. This means x - 7 is not the same as 7 - x. The position of each term determines the final result.

Practice by converting different phrases into algebraic expressions to get comfortable with the order of operations. It鈥檚 a great way to master subtraction in algebra.
using variables
Variables are symbols, usually letters, used to represent unknown values or quantities that can change. They are foundational in algebra, making it possible to write general expressions that can be solved for different values.

Here鈥檚 how to effectively use variables:
  • Choose a letter, often x, y, or z, to represent the unknown number. In our example, we chose x.
  • Use the variable to set up equations or expressions based on word problems. When the word phrase is 'seven subtracted from a number', the variable signifies 'a number' or x.
  • Substitute the variable into your mathematical equation. This makes it flexible and easy to solve for different scenarios or values.
Working with variables allows for greater generalization and abstraction in algebra, helping you solve a wide range of problems. Keep practicing with different phrases to build your confidence in using variables!

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Most popular questions from this chapter

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 4 if its last two digits form a number divisible by \(4,\) and not otherwise. Show that (a) \(6,221,464\) is divisible by 4 and \((b) 2,876,335\) is not divisible by 4

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 9 if the sum of its digits is divisible by \(9,\) and not otherwise. Show that (a) \(4,114,107\) is divisible by \(9 \quad\) and \(\quad\) (b) \(2,287,321\) is not divisible by \(9 .\)

Decide whether each statement is true or false. \(-|12|>|-15|\)

Perform each indicated operation. $$ 6-(-8+3) $$

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. \(18,12,0,-4,\) and \(-10\)
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