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Chapter 3: Problem 55

Apply the appropriate property to simplify the expression. $$6(2+x)$$

Short Answer

Expert verified
The simplified expression is \( 12 + 6x \).

Step by step solution

01

Identify the Property to Use

Recognize that the expression can be simplified using the distributive property, which states that for any numbers a, b, and c: \[ a(b + c) = ab + ac \]
02

Apply the Distributive Property

Use the distributive property to multiply both terms inside the parentheses by 6. \[ 6(2 + x) = 6 \times 2 + 6 \times x \]
03

Simplify Each Term

Multiply the constants in each term: \[ 6 \times 2 = 12 \] and \[ 6 \times x = 6x \]
04

Combine the Simplified Terms

Combine the simplified terms to get the final expression: \[ 12 + 6x \]

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Key Concepts

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

simplifying expressions
Simplifying expressions is a key skill in prealgebra. It involves reducing expressions to their simplest form by combining like terms and applying mathematical properties. The goal is to make the expression as straightforward as possible. In the given exercise, we simplified the expression \( 6(2 + x) \) using the distributive property. This approach helps transform a complex expression into a simpler one that is easier to work with. By applying the distributive property, we multiply each term inside the parentheses by 6, resulting in \( 6 \times 2 + 6 \times x \). Simplifying these terms, we get \( 12 + 6x \).
prealgebra
Prealgebra forms the foundation for algebra. It involves basic arithmetic and an introduction to algebraic thinking. One key concept in prealgebra is understanding how to manipulate expressions. For example, recognizing when to use properties like the distributive property is essential:
  • It helps in breaking down complex expressions.
  • It prepares you for solving equations in algebra.
In the exercise provided, we used the distributive property to break down the expression \( 6(2 + x) \). This is a fundamental prealgebra skill that will be used frequently as you progress in math.
multiplying terms
Multiplying terms is an integral part of simplifying expressions. When you multiply a term by a number, you apply it to each part of the term. Let's look at the provided problem:
  • The original expression is \( 6(2 + x) \).
  • Using the distributive property, we multiply 6 by each term inside the parentheses.
  • This breaks down to \( 6 \times 2 \) and \( 6 \times x \).
By performing these multiplications, we get \( 12 \) and \( 6x \). Combining these results, we end up with the simplified expression \( 12 + 6x \). Understanding how to multiply terms is crucial for both simplifying expressions and solving equations.

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