/*! 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 516 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 516

In the following exercises, solve. $$-4 w=26$$

Short Answer

Expert verified
w = -\frac{13}{2} or w = -6.5

Step by step solution

01

- Isolate the variable

First, divide both sides of the equation by -4 to isolate the variable \(w\). This involves performing the same operation on both sides of the equation to keep it balanced.
02

- Simplify the equation

After dividing both sides by -4, the equation becomes \(w = \frac{26}{-4}\).
03

- Simplify the fraction

Next, simplify the fraction \(\frac{26}{-4}\) by dividing the numerator and the denominator by their greatest common divisor, which is 2. This gives \(w = \frac{-13}{2}\).
04

- Write the final answer

The final simplified form of \(w\) is \(-\frac{13}{2}\) or -6.5.

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.

Isolate the Variable
In the given equation \-4w = 26\, our goal is to find the value of \( w \). To achieve this, we need to isolate the variable.

Isolating the variable means getting \( w \) alone on one side of the equation. In this case, \( w \) is being multiplied by -4.

To isolate \( w \), we perform the opposite operation. Since -4 is multiplied by \( w \), we divide both sides of the equation by -4. This keeps the equation balanced:

\[ \frac{-4w}{-4} = \frac{26}{-4} \]
Now we have:
\[ w = \frac{26}{-4} \]
Simplify Fractions
In our equation, we now have \( w = \frac{26}{-4} \). This fraction can be simplified.

Simplifying a fraction means making it as simple as possible while keeping its value the same.

We look for a common factor in the numerator (26) and the denominator (-4):

  • The common factor here is 2.
To simplify, we divide both the numerator and the denominator by 2:

\[ \frac{26 梅 2}{-4 梅 2} = \frac{13}{-2} \]

So, the simplified form is:

\( w = -\frac{13}{2} \)

Division in Algebra
Division in algebra follows the same basic principles as regular arithmetic. However, it can help to remember some key rules:

  • Division by a negative number will change the sign of the result.
  • Always perform the same operation on both sides of the equation to keep it balanced.
  • After dividing, simplify the resulting fraction if possible.
As we saw in the exercise, dividing both sides by -4 isolated the variable \( w \):
  • \( w = \frac{26}{-4} \)
  • Which simplified to \( w = -\frac{13}{2} \)
This illustrates the importance of proper division in solving equations.
Negative Numbers
Handling negative numbers correctly is crucial in algebra. Here are some key points:

  • When dividing by a negative number, the sign of the quotient changes. This is why \( \frac{26}{-4} \) results in a negative fraction.
  • Negative numbers can appear in different forms in algebra, such as coefficients (like -4 in -4\( w \)) or in fractions.
In our example:

  • The negative sign indicates that the value of \( w \) is less than zero.
  • Finding the correct sign is important for the solution.
Understanding and correctly managing negative numbers ensures that your solution is accurate and avoids mistakes.

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

In the following exercises, simplify. $$ \frac{2^{3}-2^{2}}{\left(\frac{3}{4}\right)^{2}} $$

In the following exercises, simplify. $$ \frac{7}{11} \div\left(-\frac{7}{11}\right) $$

In the following exercises, perform the indicated operations and simplify. $$\frac{1}{5}+\frac{2}{3}$$

In the following exercises, perform the indicated operations and simplify. $$\frac{11}{12}-\frac{2}{3}$$

In the following exercises, translate and solve. The quotient of \(p\) and \(-4\) is \(-8 .\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.