/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 70 Use the distributive property to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 70

Use the distributive property to rewrite each expression. $$ 5(w+4) $$

Short Answer

Expert verified
5(w+4) = 5w + 20

Step by step solution

01

Identify the Terms

The expression given is \( 5(w+4) \). Identify the terms inside the parentheses, which are \( w \) and 4.
02

Apply the Distributive Property

Use the distributive property \( a(b+c) = ab + ac \) to rewrite the expression. In this case, let \( a = 5 \), \( b = w \), and \( c = 4 \).
03

Distribute the Multiplication

Multiply 5 by each term inside the parentheses individually: \( 5 \times w = 5w \) and \( 5 \times 4 = 20 \).
04

Combine the Results

Combine the distributed terms to get the final expression: \( 5w + 20 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Algebraic Expressions
In algebra, expressions are like sentences that use numbers, variables, and operations. An algebraic expression can have constants (like 4), variables (like w), and coefficients (like 5 in 5w). Variables represent unknown values that can change. They are usually letters such as w, x, or y.
For example, in the expression 5(w + 4), we have:
  • Coefficient: 5
  • Variable: w
  • Constant: 4
Algebraic expressions can be rearranged and simplified using various properties and rules, including the distributive property. Understanding these basic components helps in manipulating and solving equations efficiently.
Simplifying Expressions
Simplifying an algebraic expression means making it easier to understand or solve. This involves combining like terms, using the distributive property, and reducing the expression to its simplest form. The goal is to convert a complex expression into a simpler one.
For instance, in our original example, we start with 5(w+4). By using the distributive property, we can make it simpler and more manageable:
1. Distribute the 5 to both w and 4.
2. This gives us 5w + 20.
Simplifying helps us solve equations faster and understand the relationships between different terms.
Multiplication
Multiplication in algebra often involves distributing a number over a sum or difference inside parentheses. This is where the distributive property plays a crucial role.
When you see an expression like 5(w + 4), you need to multiply the 5 by each term inside the parentheses:
\( 5 \times w = 5w \)
\( 5 \times 4 = 20 \)
Multiplication also follows certain rules: the order in which you multiply numbers doesn't change the result. This is known as the commutative property of multiplication.
By distributing and multiplying correctly, you rearrange and simplify expressions, making it easier to solve algebraic problems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write a numerical expression for each phrase, and simplify the expression. The sum of -7 and -13 , increased by 14

Use the distributive property to rewrite each expression. $$ -\frac{1}{5}(5 x-7) $$

Use the distributive property to rewrite each expression. $$ 7(z-8) $$

Use the distributive property to rewrite each expression. $$ -\frac{2}{5}(10 b+20 a) $$

Solve each problem. Nadine enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were $$ \begin{array}{lllll} -19, & 28, & -5, & \text { and } & 13 . \end{array} $$ What was her final score for the four turns?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.