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Chapter 1: Problem 8

$$\text { Simplify the given algebraic expressions.}$$ $$-4 C+L-6 C$$

Short Answer

Expert verified
The expression simplifies to \(-10C + L\).

Step by step solution

01

Identify Like Terms

In the expression y -=4C + L - 6C, identify which terms are alike. The terms that contain the variable $C$ are like terms, those are $-4C$ and $-6C$. $
02

Combine Like Terms

Add the coefficients of the like terms $-4C$ and $-6C$ together: $-4C - 6C = (-4 - 6)C = -10C$. This simplifies the expression to $-10C + L$.
03

Final Simplified Expression

Combine the result from the like terms with any other terms: Since there are no like terms for $L$, you retain it in the expression. Thus, the final simplified expression is: $-10C + L$.

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Key Concepts

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

Understanding Like Terms
In algebra, like terms are an essential concept to grasp. Like terms are terms within an expression that have the same variable part. This means that the variables and any exponents on these variables must match exactly. In the expression \(-4C + L - 6C\), the terms \(-4C\) and \(-6C\) are like terms because they both contain the variable \(C\).
  • Terms like \(L\) are not considered like terms with those containing \(C\), as they represent different variables.
  • It's important to only combine terms that are alike.
Identifying like terms is the first step in simplifying algebraic expressions.
Working with Coefficients
Coefficients are the numerical part of the terms in an algebraic expression. They indicate how many times the variable is being multiplied. In \(-4C + L - 6C\), \(-4\) and \(-6\) are the coefficients of the terms \(-4C\) and \(-6C\) respectively.
To simplify the expression, you must add or subtract these coefficients. When dealing with like terms, you add or subtract their coefficients, keeping the variable part the same.
  • For \(-4C\) and \(-6C\), you perform the operation \(-4 - 6\), resulting in \(-10\).
  • This gives a new term \(-10C\). This is because \(-4\) and \(-6\) are simply numbers that tell you how many \(C\)'s you have.
This step is crucial for reducing an expression to its simplest form.
Simplification of Algebraic Expressions
Simplification in algebra involves reducing expressions to their simplest form. This process makes equations easier to solve or understand.
After identifying and combining like terms in \(-4C + L - 6C\), the expression was simplified to \(-10C + L\). Steps in simplification typically include:
  • Identifying like terms and combining them.
  • Summing or subtracting their coefficients properly as shown in earlier steps.
Ensuring there are no further operations to be performed, the final form \(-10C + L\) is reached. This simplified expression uses fewer terms, making it easier to interpret and work with.

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