/*! 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 56 Solve the equations. $$\frac{w... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 56

Solve the equations. $$\frac{w}{6}=-18$$

Short Answer

Expert verified
w = -108

Step by step solution

01

- Understand the equation

The given equation is \( \frac{w}{6} = -18 \). This indicates that when w is divided by 6, the result is -18.
02

- Isolate the variable w

To solve for w, we need to get rid of the denominator 6. Multiply both sides of the equation by 6:
03

- Perform the multiplication

Multiply both sides of the equation by 6: \( \frac{w}{6} \times 6 = -18 \times 6 \). This simplifies to \( w = -108 \).

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.

Understanding Algebra
Algebra is like a puzzle where we use letters to represent numbers. These letters are called variables. For example, in the equation \( \frac{w}{6} = -18 \), 'w' is the variable.

The goal in algebra is often to solve for the variable, which means finding the value of the letter.

There are rules we follow to solve these puzzles, like performing the same operation to both sides of the equation to keep it balanced.
Isolating Variables
To solve an equation, we need to get the variable by itself on one side of the equation. This is known as isolating the variable.

In the equation \( \frac{w}{6} = -18 \), 'w' is divided by 6. To isolate 'w', we need to do the opposite operation of division, which is multiplication.

We multiply both sides of the equation by 6 to cancel out the division by 6. This leaves us with 'w' by itself.

\( \frac{w}{6} \times 6 = -18 \times 6 \) simplifies to \( w = -108 \).
Multiplication in Equations
Multiplication is a key operation in solving equations. When we multiply both sides of an equation by the same number, the balance of the equation is maintained.

For example, in our problem, we multiplied both sides by 6 because the variable 'w' was divided by 6. This is an important step called 'clearing the fraction.'

Here鈥檚 the multiplication step again: \( \frac{w}{6} \times 6 = -18 \times 6 \), which simplifies to \( w = -108 \).

This process helps us find the value of the variable, solving the equation.

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

How many fifths are in \(2 \frac{3}{5} ?\)

Simplify the fraction to lowest terms. Write the answer as a fraction or a whole number. $$\frac{34}{85}$$

How many sixths are in 2?

Convert the mixed number to an improper fraction. $$12 \frac{1}{6}$$

Simplify the fraction to lowest terms. Write the answer as a fraction or a whole number. $$\frac{77}{110}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete 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.