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Chapter 10: Problem 95

Perform each indicated operation. See Sections 2.1 and 5.4. $$ 6 x+8 x $$

Short Answer

Expert verified
The simplified expression is \(14x\).

Step by step solution

01

Understand the Expression

The problem presents the expression \(6x + 8x\). This involves adding two like terms with the same variable, \(x\).
02

Combine Like Terms

Like terms have the same variable raised to the same power. Here, both terms have \(x\) raised to the power of 1. Combine the coefficients of these like terms by adding them together: \(6 + 8\).
03

Simplify the Expression

Add the coefficients from Step 2: \(6 + 8 = 14\). So, the expression simplifies to \(14x\).

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Key Concepts

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

Understanding Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and operators. They can represent a wide range of mathematical relationships. In the expression "\(6x + 8x\)", the numbers \(6\) and \(8\) are coefficients. The \(x\)s are variables, which represent unknown values.
When working with algebraic expressions, it鈥檚 important to identify the components:
  • Coefficients: Numbers multiplying the variables.
  • Variables: Symbols like \(x\), which can change.
  • Operators: Symbols like \(+, -\), used to perform operations.
Recognizing these components helps you manipulate and simplify the expressions effectively.
Identifying Like Terms
Like terms in algebra are terms that have the same variable raised to the same power. This means their only difference is in the coefficients. In the expression "\(6x + 8x\)", both terms are like terms because:
  • They each have the variable \(x\).
  • The variable \(x\) is raised to the same power, which is 1 in both cases.
By identifying like terms, you can simplify expressions by combining them. Check for like terms before performing operations. This ensures that you are only combining terms that are truly like terms.
Simplifying Algebraic Expressions
Simplification in algebra involves reducing expressions to their simplest form. This process makes them easier to work with and understand. To simplify something like "\(6x + 8x\)", you need to:
  • Combine the coefficients: Adding the numbers in front of the variables (\(6\) and \(8\)), gives you \(14\).
  • Attach the variable: Since you鈥檙e dealing with like terms, simply rewrite the variable \(x\) alongside the new coefficient.
The result is "\(14x\)", a simpler form of the original expression. Simplification relies on understanding like terms and performing operations correctly, allowing you to handle more complex algebraic problems with ease.

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