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Chapter 2: Problem 80

Simplify by combining like terms whenever possible. $$18+6 w-w+4$$

Short Answer

Expert verified
22 + 5w

Step by step solution

01

Identify Like Terms

First, identify the like terms in the expression. Here we have constants and terms with the variable \(w\). The constants are \(18\) and \(4\), and the terms with the variable \(w\) are \(6w\) and \(-w\).
02

Combine Constant Terms

Add the constant terms together: \(18 + 4 = 22\).
03

Combine Variable Terms

Combine the variable terms: \(6w - w = 5w\).
04

Write the Simplified Expression

Combine the simplified constant and variable terms into a single expression: \(22 + 5w\).

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Key Concepts

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

like terms
Like terms are algebraic terms that have the same variables raised to the same power. When you're simplifying expressions, identifying like terms is crucial.
In the given exercise, we have two types of terms:
  • Constants (numbers without variables): 18 and 4.
  • Variable terms (terms with the variable): 6w and -w.
Recognizing like terms helps us combine them effectively for more straightforward calculations.
In our example, the like terms were grouped as constants together and variable terms together.
combining terms
Combining terms involves adding or subtracting like terms to simplify an algebraic expression. Once the like terms are identified, you can combine them by performing the arithmetic operations.
Here's how we combined the terms in the problem:
  • Combining the constants: 18 + 4 = 22.
  • Combining the variable terms: 6w - w = 5w.
After combining the terms, the simplified expression is written by combining the results of both:
22 + 5w.
This process reduces the complexity of the expression, making it easier to understand and work with.
constants and variables
Understanding the difference between constants and variables is essential in algebra. Constants are fixed values that do not change. In our exercise, 18 and 4 are constants.
Variables, on the other hand, are symbols that represent unknown values and can change. In our expression, 'w' is the variable.
By separating constants and variables, we can simplify the expression efficiently. Constants can be combined through basic arithmetic.
Variable terms are combined by considering their coefficients. In the example, 6w and -w were combined to give 5w.
Recognizing and handling these parts correctly ensures accurate and efficient simplification of algebraic expressions.

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