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Chapter 11: Problem 18

Specify each term. $$8 s+2 r-7 t$$

Short Answer

Expert verified
The terms are \(8s\), \(2r\), and \(-7t\).

Step by step solution

01

Identify the Terms

The expression given is \(8s + 2r - 7t\). Here, we need to identify each term. In algebra, terms in an expression are the individual components separated by plus or minus signs. Thus, the terms in this expression are \(8s\), \(2r\), and \(-7t\).
02

Specify Each Term

Now, let's specify each term:- The first term \(8s\) consists of a coefficient \(8\) and a variable \(s\).- The second term \(2r\) consists of a coefficient \(2\) and a variable \(r\).- The third term \(-7t\) consists of a coefficient \(-7\) and a variable \(t\). The negative sign is part of the coefficient.

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Key Concepts

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

Terms in Algebra
In algebra, understanding terms is crucial since they form the building blocks of any algebraic expression. Essentially, a term is a single mathematical component that can comprise numbers, variables, or both combined. They are separated by plus "+" or minus "-" signs in an expression.
To simplify, think of terms as individual pieces of a puzzle that come together to form a complete picture. In the expression \(8s + 2r - 7t\):
  • Each of these parts is a term: \(8s\), \(2r\), and \(-7t\).
  • Notice that terms can be positive, negative, or even zero.
  • The signs "\(+\)" and "\(-\)" highlight the separation and relationship between different terms.
Understanding terms help one to grasp the structure of algebraic expressions better, which is pivotal for simplifying, evaluating, and manipulating algebraic expressions.
Coefficients in Algebra
Coefficients play an essential role in understanding algebraic terms. A coefficient is the numerical factor that multiplies a variable within a term. It's important because it tells you "how much" of the variable you're dealing with.
Let鈥檚 break down the expression \(8s + 2r - 7t\):
  • In the term \(8s\), "8" is the coefficient, which means "8 times the variable \(s\)".
  • In \(2r\), the coefficient is "2" and implies "2 times the variable \(r\)".
  • Similarly, in \(-7t\), "-7" acts as the coefficient indicating "negative 7 times the variable \(t\)".
It鈥檚 crucial to understand that the coefficient speaks volumes about the magnitude and direction (negative or positive) in relation to the variable it multiplies. This understanding aids greatly in comparing and performing operations on expressions.
Variables in Algebra
Variables form the backbone of algebra, representing unknown or general numbers in expressions and equations. They are typically denoted by letters such as \(s\), \(r\), and \(t\) in our example. Variables allow flexibility and generalization in mathematics.
Here鈥檚 how variables function in the expression \(8s + 2r - 7t\):
  • In \(8s\), \(s\) is the variable, which means this term is flexible and can represent any number when needed.
  • Likewise, \(r\) acts as the variable in the term \(2r\), representing an unspecified or variable quality.
  • The term \(-7t\) contains the variable \(t\), again indicating that it can assume different numerical values.
Variables allow us to write formulas, create functions, and even solve problems without immediately knowing exact numerical values. Mastering variables gives students the power to explore endless mathematical possibilities.

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Most popular questions from this chapter

For problems \(57-140\), solve each equation. $$ 3 x+2=7 $$

Translate each phrase or sentence to a mathematical expression or equation. Thirteen less than some number is equal to three times the number added to eight.

Translate each phrase or sentence to a mathematical expression or equation. A number divided by seven, plus two, is seventeen.

For problems \(57-140\), solve each equation. $$ x-5=-6 $$

Translate each phrase or sentence to a mathematical expression or equation. A number is subtracted from nine. This result is then increased by one. The result is eight more than three times the number.
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