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Chapter 1: Problem 5

\(14 k+9 k-k\)

Short Answer

Expert verified
The simplified expression is \(22k\).

Step by step solution

01

Combine like terms

Identify the like terms in the expression. Here, all terms are multiples of the same variable, which is k: \(14k + 9k - k\).
02

Perform addition

First, add the positive terms together: \(14k + 9k = 23k\).
03

Subtract the remaining term

Subtract the last term from the result of the addition: \(23k - k = 22k\).

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Key Concepts

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

Elementary Algebra
Elementary algebra is the branch of mathematics that deals with the basic operations and properties of numbers. Here, you often work with unknown values represented by letters such as x, y, or k. These letters are called variables.

Understanding how to manipulate these variables is crucial in solving algebraic expressions and equations.

In elementary algebra, you learn to combine like terms, perform basic arithmetic operations, and simplify expressions.
Variable Expressions
A variable expression is a mathematical phrase that includes numbers, operations, and variables. For example, the expression given in the exercise, \[14k + 9k - k\], is a variable expression.

In this expression:
  • 14, 9, and the implied 1 before k are coefficients (numbers multiplying the variable).
  • k is the variable.


To simplify variable expressions, you must understand the concept of combining like terms. Like terms are terms that have the same variable raised to the same power. In this case, all terms have the variable k, making them like terms.
Simplifying Equations
Simplifying equations is a fundamental skill in algebra. It involves reducing an equation to its simplest form. Here鈥檚 how you can simplify the given expression step-by-step:

1. Identify like terms: In \(14k + 9k - k\), all terms involve the variable k.
2. Add the like terms: Combine the positive coefficients first. Here, you add 14k and 9k to get 23k: \[14k + 9k = 23k\].
3. Subtract the remaining term: Finally, subtract k from 23k: \[23k - k = 22k\].

Thus, the simplified form of the expression is \(22k\). Simplifying equations helps you solve for unknown variables more easily, making it a critical skill in algebra.

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