/*! 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 50 Solve using the multiplication p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 50

Solve using the multiplication principle. Don't forget to check! $$ -3 x=5 $$

Short Answer

Expert verified
x = -\frac{5}{3}

Step by step solution

01

- Identify the equation

The given equation is \( -3x = 5 \)
02

- Apply the multiplication principle

To isolate \( x \), divide both sides of the equation by -3: \[ x = \frac{5}{-3} \]
03

- Simplify the solution

Simplify the fraction: \[ x = -\frac{5}{3} \]
04

- Verify the solution

Substitute \( x = -\frac{5}{3} \) back into the original equation to check: \[ -3 \times -\frac{5}{3} = 5 \] \[ 5 = 5 \] The solution 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.

multiplication principle
The multiplication principle is a fundamental concept in algebra. It states that you can multiply both sides of an equation by the same non-zero number without changing the equation's solution. This principle helps isolate the variable you are trying to solve for. For instance, in the exercise, we have the equation \( -3x = 5 \). To isolate \( x \), you can divide both sides by \( -3 \), as division is the same as multiplying by the reciprocal.
solving equations
Solving equations involves finding the value of the variable that makes the equation true. Step-by-step, it looks like this:
  • Identify the equation: The first step is to clearly see what you are dealing with. In our case, it's \( -3x = 5 \).
  • Apply algebraic principles: Use strategies such as the multiplication principle to isolate the variable. For \( -3x = 5 \), divide by \( -3 \) to get \( x = \frac{5}{-3} \).
  • Verify the solution: Plug the value back into the original equation to ensure it works. This involves checking if \( -3 \times \frac{-5}{3} = 5 \). Indeed, it does, confirming our solution is correct.
This structured approach ensures you don't miss any important steps and helps avoid errors.
fraction simplification
Fraction simplification makes equations easier to read and understand. After isolating the variable, the next step often involves simplifying fractions. For example, from \( x = \frac{5}{-3} \), we simplify to \( x = -\frac{5}{3} \). Simplifying fractions might involve reducing the numerator and denominator to their smallest forms or recognizing common factors.
In our solved example, no further reduction is necessary since 5 and 3 are already in their simplest form. But always check your fractions to ensure clarity in your final answer.

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 is the use of statistics in each of the following misleading? a) A business explaining new restrictions on sick leave cited a recent survey indicating that \(40 \%\) of all sick days were taken on Monday or Friday. b) An advertisement urging summer installation of a security system quoted FBI statistics stating that over \(26 \%\) of home burglaries occur between Memorial Day and Labor Day.

Translate to an inequality. The age of the Mayan altar exceeds 1200 yr.

Use an inequality and the five-step process to solve each problem. The U.S. Postal Service defines a "package" as a parcel for which the sum of the length and the girth is less than 84 in. (Length is the longest side of a package and girth is the distance around the other two sides of the package.) A box has a fixed girth of 29 in. Determine (in terms of an inequality) those lengths for which the box is considered a "package." (THE IMAGE CANNOT BE COPY)

Use an inequality and the five-step process to solve each problem. If \(f\) represents Fran's age and \(w\) represents Walt's age, write a sentence that would translate to \(w+3

Use an inequality and the five-step process to solve each problem. Reduced Fat Oreo " cookies contain 4.5 of fat per serving. In order for a food to be labeled "reduced fat," it must have at least \(25 \%\) less fat than the regular item. What can you conclude about the number of grams of fat in a serving of the regular Oreo cookies?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics 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.