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Chapter 2: Problem 70

Write each phrase as an algebraic expression. \(-150\) added to \(c\)

Short Answer

Expert verified
c - 150

Step by step solution

01

Identify the Numbers and Variable

Notice that the given numbers and variable are -150 and c respectively.
02

Choose the Mathematical Operation

The phrase 'added to' suggests that you will be using the addition operation.
03

Write the Algebraic Expression

Combine the variable and number with the addition operation: \[c + (-150)\]

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Key Concepts

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

Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols.
These symbols, often represented by letters, stand in for numbers in equations and expressions.
When you see a problem like 'Write -150 added to c as an algebraic expression,' you're working within the realm of algebra.
Let's break it down:
  • We use letters (variables), like 'c,' to represent unknown or changeable values.
  • We use numbers to represent fixed values.
  • And we use operations (like addition) to combine these numbers and variables.
Algebra is all about finding the balance and relationships between these numbers and variables. It's a fundamental part of higher mathematics and is widely used in various real-world applications, such as engineering, economics, and science.
Addition Operation
The addition operation is one of the basic arithmetic operations.
It combines two numbers to get their total sum.
When the phrase 'added to' is used in algebra, it suggests that you need to add the given values.
In this exercise, 'added to' means you need to add \(c\) and \(-150\):
\[ c + (-150) \]
Adding a negative number is similar to subtraction.
So, \(c + (-150)\) means the same as \(c - 150\).
Here are some key points about addition in algebra:
  • Adding a positive number increases the value.
  • Adding a negative number decreases the value.
  • The order of addition does not matter (commutative property).
This operation helps to form and solve algebraic expressions, which is a crucial skill in algebra.
Variables
Variables are symbols used to represent unknown or changing quantities in algebra.
They are usually denoted by letters such as \(x, y, z,\) or in this exercise, \(c\).
Variables allow us to write general expressions and equations that can represent many different situations.
Let's look closer at variables in algebra:
  • Variables can represent numbers we don't yet know.
  • They enable us to write formulas and equations that solve real problems.
  • Combining variables with numbers and operations gives us algebraic expressions.
In our exercise, \(c\) is the variable.
We combine it with a number using an addition operation to form the algebraic expression \(c + (-150)\).
Understanding variables is essential because they help generalize mathematical concepts, making it easier to solve complex problems.

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Most popular questions from this chapter

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$a \cdot|b|$$

Rank the numbers from least to greatest. If \(a\) represents a negative number, then what is the sign of \(-a ?\)

Translate each English phrase to a mathematical expression. Then simplify. Subtract 12 from 5

Jeff's balance in his checking account was 2036 dollar at the beginning of the week. During the week, he wrote two checks, made two deposits, and made one ATM withdrawal. What is his ending balance? $$\begin{array}{l|r} \hline \text { Check } & -\$ 150 \\ \hline \text { Check } & -\$ 25 \\ \hline \text { Paycheck (deposit) } & \$ 480 \\ \hline \text { ATM } & -\$ 200 \\ \hline \text { Cash (deposit) } & \$ 80 \\ \hline \end{array}$$

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$-|a|$$
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