/*! 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 307 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 307

In the following exercises, solve the equation. $$ -1.7 c=8.5 $$

Short Answer

Expert verified
The solution is \( c = -5 \).

Step by step solution

01

- Isolate the variable

To isolate the variable, we need to get rid of the coefficient (which is -1.7 in this case) that is attached to the variable. We do this by dividing both sides of the equation by -1.7: \[ c = \frac{8.5}{-1.7} \]
02

- Solve the division

Now, perform the division to find the value of \(c\). Let's compute it: \[ c = \frac{8.5}{-1.7} = -5 \]

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.

Variables and Coefficients
Understanding variables and coefficients is crucial when solving linear equations.
In the equation given, \(-1.7c = 8.5\), the variable is \(c\). A variable is a symbol (usually a letter) that represents an unknown number.
Here, \(c\) can be any number, and our goal is to find out what that number is.
The coefficient is the number that multiplies the variable. In this case, \(-1.7\) is the coefficient for \(c\).
Coefficients can be positive or negative numbers.
To solve for \(c\), we need to understand how to work with these coefficients properly.
Isolating the Variable
The first step in solving an equation like \(-1.7c = 8.5\) is to isolate the variable.
Isolating the variable means getting the variable \(c\) by itself on one side of the equation.
To do this, we need to undo the operation being done to \(c\).
Since \(-1.7\) is being multiplied by \(c\), we need to perform the opposite operation, which is division.
By dividing both sides of the equation by the coefficient \(-1.7\), we can isolate the variable.
This step simplifies the equation to: \[ c = \frac{8.5}{-1.7} \]
Division
Once the variable \(c\) is isolated, the next step is to perform the division.
Division is one of the basic arithmetic operations and is symbolized by the fraction line \(/\) or division symbol \(\).
In our equation, we have: \[ c = \frac{8.5}{-1.7} \]
To solve this, we divide 8.5 by -1.7.
It鈥檚 helpful to remember that dividing a positive number by a negative number will always give a negative result.
Performing the division, we get: \[ c = -5 \]
Therefore, the solution to the equation \(-1.7c = 8.5\) is \(c = -5\).

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, find the unit rate. Round to two decimal places, if necessary. 54 beats in 0.5 minute

In the following exercises, find the unit rate. Round to two decimal places, if necessary. 180 calories per 16 ounces

Sales Tax Hyo Jin lives in San Diego. She bought a refrigerator for \(\$ 1624.99\) and when the clerk calculated the sales tax it came out to exactly \(\$ 142.186625\) Round the sales tax to the nearest (a) penny (b) dollar.

approximate the (a) circumference and (b) area of each circle. If measurements are given in fractions, leave answers in fraction form. diameter \(=\frac{3}{4} \mathrm{m}\)

In the following exercises, round each number to the nearest hundredth. $$0.761$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Pure 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.