/*! 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 39 Solve each equation, and check y... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 39

Solve each equation, and check your solution. $$ \frac{2}{5} w-6=\frac{7}{5} w $$

Short Answer

Expert verified
w = -6

Step by step solution

01

Isolate the variable term on one side

Subtract \( \frac{2}{5} w \) from both sides of the equation to get all the terms involving w on one side. This gives us: \[-6 = \frac{7}{5} w - \frac{2}{5} w \]
02

Combine like terms

Combine the terms involving w on the right-hand side: \[-6 = \left( \frac{7}{5} - \frac{2}{5} \right) w \] This simplifies to: \[-6 = \frac{5}{5} w = w \]
03

Solve for the variable

The equation simplifies to: \[-6 = w \] Therefore, \( w = -6 \)
04

Check the solution

Substitute \( w = -6 \) back into the original equation to ensure it is correct: \[\frac{2}{5}(-6) - 6 = \frac{7}{5}(-6) \] Simplifying both sides, we get: \[-\frac{12}{5} - 6 = -\frac{42}{5} \] Converting \( 6 \) to a fraction with denominator 5, we have: \[-\frac{12}{5} - \frac{30}{5} = -\frac{42}{5} \] Simplifying the left-hand side: \[-\frac{42}{5} = -\frac{42}{5} \] Both sides are equal, so \( w = -6 \) is correct.

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.

Isolating the Variable
Isolating the variable is the first step in solving linear equations. The goal is to move all terms containing the variable to one side of the equation. Let's look at our exercise: \(\frac{2}{5} w - 6 = \frac{7}{5} w\). To isolate the variable, we need to subtract \(\frac{2}{5} w\) from both sides. This step helps us get all the terms involving \(w\) on one side. After performing this operation, the equation simplifies to \(-6 = \frac{7}{5} w - \frac{2}{5} w\).
Combining Like Terms
Combining like terms is crucial to simplify the equation further. In our example, we combine \(\frac{7}{5} w\) and \(\frac{2}{5} w\) on the right-hand side. Combining like terms involves adding or subtracting coefficients of the same variable. For the equation \(-6 = \frac{7}{5} w - \frac{2}{5} w\), we subtract \(\frac{2}{5} w\) from \(\frac{7}{5} w\), which results in \(\frac{5}{5} w\). Simplifying gives us \(-6 = w\). Remember, combining like terms effectively reduces the equation to a simpler form.
Substituting Back to Check Solution
After finding the solution, it is always good to substitute it back into the original equation to verify its correctness. For our example, we found that \(w = -6\). Now we substitute \(-6\) back into the original equation: \(\frac{2}{5}(-6) - 6 = \frac{7}{5}(-6)\). Simplify both sides of the equation. The left side becomes \(-\frac{12}{5} - 6\), which is \(-\frac{42}{5}\) when you express \(6\) as a fraction with the same denominator. The right side is also \(-\frac{42}{5}\). Since both sides are equal, the solution \(w = -6\) is correct. Substituting back is a reliable method to ensure your solution is accurate.

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

Convert each percent to a decimal. $$ 129 \% $$

On June \(13,\) researchers at West Okoboji Lake tagged 840 fish. A few weeks later, a sample of 1000 fish contained 18 that were tagged. Approximate the fish population to the nearest hundred.

Solve equation, and check your solution \(9 x-3 x+x=-4\)

Write each phrase as a mathematical expression using x as the variable. See Sections \(1.3,1.5\) \(1.6,\) and 1.8 The difference between \(-5\) and a number

Convert each percent to a decimal. $$ 9 \% $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

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.