/*! 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 82 \(21 w+4(6-5 w)=8\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 82

\(21 w+4(6-5 w)=8\)

Short Answer

Expert verified
w = -16

Step by step solution

01

Identify and Simplify Parentheses

Start by simplifying the expression inside the parentheses: \[4(6-5w)\].Calculate inside the parentheses first: \[6 - 5w\].
02

Distribute the Multiplication

Next, distribute the 4 across the simplified expression inside the parentheses:\[4 \times (6) - 4 \times (5w)\].This gives:\[4 \times 6 - 4 \times 5w = 24 - 20w\].
03

Combine Like Terms

Rewrite the equation with the distributed terms:\[21w + 24 - 20w = 8\].Combine the like terms \(21w\) and \(-20w\):\[21w - 20w + 24 = 8\].This simplifies to:\[w + 24 = 8\].
04

Isolate the Variable

Subtract 24 from both sides of the equation to isolate \(w\):\[w + 24 - 24 = 8 - 24\].This simplifies to:\[w = -16\].

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.

Simplifying Expressions
Simplifying expressions is often the first step in solving linear equations. This means making the expression as straightforward as possible by performing operations inside parentheses and combining like terms.

Take the expression inside the parentheses from the example: \text{4(6 - 5w)}\. We first need to calculate inside the parentheses:\(6 - 5w\). This leaves us with a simpler expression that we can distribute next.

This step lays the groundwork for solving the rest of the equation more easily.
Isolating Variables
Isolating variables means moving all terms involving the variable to one side of the equation and all constant terms to the other side.

In the exercise, we have simplified to: \(w + 24 = 8\).To isolate, subtract 24 from both sides: \(w + 24 - 24 = 8 - 24\), simplifying to: \(w = -16\).

At this stage, we have solved for the variable \(w\). This is our solution.

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

Solve each problem. The perimeter of a rectangle is \(36 \mathrm{~m} .\) The length is \(2 \mathrm{~m}\) more than three times the width. Find the length and the width of the rectangle.

Find the measure of an angle whose supplement measures \(39^{\circ}\) more than twice its complement.

Find the measure of an angle whose supplement is three times its measure.

Solve each formula for the specified variable. \(A x+B y=C\) for \(y\)

The sum of the measures of the angles of any triangle is \(180^{\circ} .\) In triangle \(A B C,\) the measure of angle \(A\) is \(141^{\circ}\) greater than the measure of angle \(B\). The measure of angle \(B\) is the same as the measure of angle \(C\). Find the measure of each angle.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.