/*! 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 36 Solve using the multiplication p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 36

Solve using the multiplication principle. Don't forget to check! $$ -3.3 y=6.6 $$

Short Answer

Expert verified
y = -2

Step by step solution

01

Understand the Multiplication Principle

The multiplication principle states that both sides of an equation can be multiplied or divided by the same nonzero number without changing the equality.
02

Isolate the Variable

To isolate the variable, divide both sides of the equation by -3.3: \[-3.3y 梅 -3.3 = 6.6 梅 -3.3\]
03

Simplify the Equation

Simplify both sides of the equation: \[y = 6.6 梅 -3.3\] Calculate the right-hand side: \[y = -2\]
04

Check the Solution

Substitute y = -2 back into the original equation to check the solution: \[-3.3(-2) = 6.6\] Calculate \[6.6 = 6.6\] Since both sides of the equation are equal, y = -2 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.

solving equations
Solving equations involves finding the value of the unknown variable that makes the equation true. In the given problem, the goal is to solve for the variable \(y\). This means we need to manipulate the equation to isolate \(y\) on one side. This process requires following specific algebraic steps and principles to ensure the solution is correct.
isolate the variable
Isolating the variable means getting the variable \(y\) alone on one side of the equation. In the given problem \(-3.3y = 6.6\), we divide both sides by \(-3.3\) to isolate \(y\). This step relies on the multiplication (or division) principle, which states that we can multiply or divide both sides of an equation by the same nonzero number without changing the equality. By dividing both sides by \(-3.3\), we simplify the equation to \(y\). Here鈥檚 how it looks:

o -3.3y 梅 -3.3 = 6.6 梅 -3.3
This simplifies to:
y = -2
check the solution
Checking the solution is a crucial step to confirm the accuracy. Once we have isolated the variable, we substitute \(y = -2\) back into the original equation to ensure it holds true. Plugging \(-2\) for \(y\) in \(-3.3y = 6.6\), we get:

-3.3(-2) = 6.6
Doing the multiplication, it simplifies to:
6.6 = 6.6
Since both sides are equal, the solution \(y = -2\) is correct. This step verifies that our algebraic manipulation was done properly.
simplify the equation
Simplifying the equation means performing the arithmetic operations to reduce it to its simplest form. In this problem, after isolating \(y\) by dividing both sides by \(-3.3\), we need to perform the division:

o y = 6.6 梅 -3.3
Calculating this gives:
y = -2
This final step ensures that the problem is simplified completely, and we have the solution in its simplest form. Simplifying helps in understanding and verifying the solution easily.

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

Find the volume of a rectangular solid of length \(1.3 \mathrm{~cm},\) width \(10 \mathrm{~cm}\), and height \(2.4 \mathrm{~cm}\).

Solve using the multiplication principle. Don't forget to check! $$ -\frac{1}{3} t=7 $$

Solve. $ 13-(2 c+2)=2(c+2)+3 c $$

Solve using the multiplication principle. Don't forget to check! $$ -\frac{3}{2} r=-\frac{27}{4} $$

Solve. $$ 0.8-4(b-1)=0.2+3(4-b) $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

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.