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Chapter 2: Problem 49

Use the distributive property to combine similar terms. \(-2 x+6 x\)

Short Answer

Expert verified
The expression simplifies to \(4x\).

Step by step solution

01

Identify the Terms

The expression given is \(-2x + 6x\). In this expression, the terms \(-2x\) and \(6x\) are similar because they both have \(x\) as a variable.
02

Apply the Distributive Property

The distributive property allows us to factor out common terms to simplify expressions. Here, \(x\) is the common variable, so rewrite the expression as \(x(-2 + 6)\).
03

Perform the Calculation Inside the Parentheses

Calculate the expression inside the parentheses: \(-2 + 6 = 4\).
04

Simplify the Expression

Now, multiply the factored out term \(x\) by the result from Step 3: \(x \times 4 = 4x\). The expression simplifies to \(4x\).

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Key Concepts

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

Combining Like Terms
When dealing with algebraic expressions, combining like terms is a crucial skill. Like terms are terms that have the same variable raised to the same power. In the expression \(-2x + 6x\), both terms have the variable \(x\). This commonality permits us to combine them.
By adding or subtracting the coefficients of these terms, we merge them into a single term. Here, you add the coefficients \(-2\) and \(6\) to get \(4\). Therefore, \(-2x + 6x = 4x\).
This method not only simplifies the expression but also prepares it for further mathematical operations.
Factoring Expressions
Factoring expressions involves breaking down an expression into multiple components that can multiply together to form the original expression. In the context of combining like terms, this means identifying common factors and simplifying the expression.
Within \(-2x + 6x\), \(x\) is a common factor. You can rewrite the expression to emphasize this factor: \(x(-2 + 6)\). This application of the distributive property allows us to express the sum more compactly.
Factoring is useful for recognizing common patterns in expressions, making solving algebraic equations much more manageable.
Simplifying Algebraic Expressions
Simplifying algebraic expressions involves reducing them to their simplest form. This process often includes combining like terms, factoring, and performing basic arithmetic operations. The goal is to make the expression more accessible for additional calculations.
For example, in \(-2x + 6x\), after combining like terms, you end up with \(4x\), which is simpler and easier to work with.
Whenever you're tasked with simplifying, look for opportunities to apply these techniques. This not only clears up the expression but also clarifies an otherwise complex problem, allowing you to focus on solving it efficiently.

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Most popular questions from this chapter

Subtract. $$156-(-243)$$

Perform the indicated operations. $$(6+1)(9-4)$$

Add or subtract. $$10-5-3+4$$

In Chapter 1 we defined an arithmetic sequence as a sequence of numbers in which each number, after the first number, is obtained from the previous number by adding the same amount each time. Find the next two numbers in each arithmetic sequence below. $$10,5,0, \dots$$

Apply the distributive property to each expression and then simplify the result. $$5(6+7)$$
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