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Chapter 7: Problem 25

Simplify. $$ 2 x+4+2 $$

Short Answer

Expert verified
The simplified expression is \(2x + 6\).

Step by step solution

01

Identify the Terms

We begin by identifying the terms in the expression. The expression given is \(2x + 4 + 2\), which consists of three terms: a term containing \(x\) and two constant terms.
02

Combine Like Terms

To simplify, we look for like terms that can be combined. The expression \(2x + 4 + 2\) has two constant terms: 4 and 2. We can add these two constants together to simplify the expression.
03

Perform the Arithmetic

Combine the constant terms: \(4 + 2 = 6\). This results in the expression being simplified to \(2x + 6\).
04

Write the Final Simplified Expression

After adding the constants, we are left with the simplified expression: \(2x + 6\). This expression cannot be simplified further because it contains no more like terms.

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Key Concepts

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

Understanding Like Terms
When simplifying algebraic expressions, the idea of "like terms" is essential. Like terms are terms in an expression that have the same variables raised to the same power. In the expression \(2x + 4 + 2\), \(2x\) is a term with the variable \(x\), while \(4\) and \(2\) are constant terms without a variable.
To simplify, group terms by their similarities. Here, your focus would be on recognizing that all constant numbers form a group of like terms. When you identify them, like terms can be added or subtracted to simplify the expression, as we see with \(4\) and \(2\) which combine to form \(6\).
Performing Arithmetic Operations
Arithmetic operations like addition, subtraction, multiplication, and division are the foundational tools we use to simplify expressions. Once you've identified like terms, use these operations to combine them.
In this specific problem, after grouping the constant terms \(4 + 2\), we apply the addition operation, arriving at \(6\). This step is straightforward but crucial, as it reduces the number of terms and makes the expression simpler: \(2x + 6\).
Remember, the goal of arithmetic is to streamline complex expressions, so always look for opportunities to apply these operations to simplify your work.
Role of Constant Terms
In algebraic expressions, constant terms are numbers without attached variables. They play a crucial role in simplifying expressions simply by combining them through arithmetic operations.
For the expression \(2x + 4 + 2\), the constants are \(4\) and \(2\). Since they are like terms, we added them as part of our arithmetic operations. Simplifying constant terms often can take what seems like a daunting equation and reduce it to its most basic form.
Even though constants don鈥檛 have variables, their presence helps set the groundwork for balancing equations and making equations easier to solve or understand.

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