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Chapter 1: Problem 802

Simplify using the distributive property. $$ 18-4(x+2) $$

Short Answer

Expert verified
10 - 4x

Step by step solution

01

- Identify the expression inside the parentheses

Locate the part of the expression inside the parentheses: \((x+2)\)
02

- Distribute the constant outside the parentheses

Distribute the constant -4 to each term inside the parentheses. The expression becomes: \[18 - 4 \times x - 4 \times 2\]
03

- Perform the multiplication

Multiply -4 by each term inside the parentheses: \[18 - 4x - 8\]
04

- Combine like terms

Combine the constant terms (18 and -8): \[18 - 8 - 4x\]This simplifies to: \[10 - 4x\]

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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 an essential skill in algebra. It means making the expression as simple as possible without changing its value. To simplify an expression, you may need to:
  • Use the distributive property
  • Combine like terms
For example, in the expression \(18 - 4(x + 2)\), we first use the distributive property to remove the parentheses. Then, we combine like terms to reach the simplest form.
algebraic-expressions
Algebraic expressions are combinations of numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division. For instance, the expression \(18 - 4(x + 2)\) consists of:
  • Constants: 18 and -4
  • Variable: x
  • Arithmetic operations: subtraction and multiplication
Understanding how to work with algebraic expressions is crucial for solving equations and simplifying complex problems.
combining-like-terms
Combining like terms is a method of simplifying algebraic expressions by merging terms that have the same variable. For instance, in the expression \(18 - 4(x + 2)\), after distributing -4, we get \(18 - 4x - 8\). Here, 18 and -8 are like terms because they are both constants. By combining them, the expression simplifies to \(10 - 4x\). This step is crucial for reducing expressions to their simplest form.

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