/*! 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 38 Solve using the addition princip... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 38

Solve using the addition principle. Don't forget to check! $$ y+5.3=8.7 $$

Short Answer

Expert verified
y = 3.4

Step by step solution

01

Identify the Equation

The given equation is: \[ y + 5.3 = 8.7 \]
02

Isolate the Variable

Use the addition principle to isolate the variable y. To do this, subtract 5.3 from both sides of the equation:\[ y + 5.3 - 5.3 = 8.7 - 5.3 \]This simplifies to:\[ y = 3.4 \]
03

Verify the Solution

Substitute the value of y back into the original equation to verify the solution:\[ y + 5.3 = 8.7 \]Substitute \( y = 3.4 \):\[ 3.4 + 5.3 = 8.7 \]Calculate the left side:\[ 8.7 = 8.7 \]Since both sides of the equation are equal, the solution is verified.

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.

The Addition Principle and How It Works
The addition principle is a fundamental concept in algebra that helps us solve equations by maintaining their balance. Imagine a seesaw, where both sides need to be equal in weight for it to stay level. Similarly, in an equation, whatever we do to one side, we have to do to the other.
In the given exercise, we need to isolate the variable y. The equation is: onumber y + 5.3 = 8.7 . According to the addition principle, to remove 5.3 from the left side, we subtract it from both sides: \[ y + 5.3 - 5.3 = 8.7 - 5.3 \]
This ensures the balance of the equation. Simplifying both sides, we get: \[ y = 3.4 \] This is our solution using the addition principle.
Isolating Variables in Algebraic Equations
Isolating the variable means getting the variable by itself on one side of the equation. In this case, the variable is y.
To isolate y, we need to move all other numbers to the opposite side of the equation. In the equation \[ y + 5.3 = 8.7 \], we isolate y by eliminating + 5.3 from the left-hand side.
We do this by using the addition principle and subtracting 5.3 from both sides. The step looks like this: \[ y + 5.3 - 5.3 = 8.7 - 5.3 \]
This simplifies to \[ y = 3.4 \], meaning we have successfully isolated the variable y.
When isolating variables, remember to perform the same operation on both sides to keep the equation balanced.
Verifying Solutions to Ensure Accuracy
After solving for a variable, it鈥檚 always important to verify your solution. Verification ensures that your solution is correct and satisfies the original equation.
For this exercise, we found that y = 3.4. To verify, we substitute y back into the original equation: \[ y + 5.3 = 8.7 \] Plugging 3.4 for y, we get: \[ 3.4 + 5.3 = 8.7 \]
Simplifying the left-hand side, we see that \[ 8.7 = 8.7 \]. Since both sides are equal, we have confirmed our solution is correct.
Verification is a quick and reliable way to check your work and ensure you have the correct 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

Use an inequality and the five-step process to solve each problem. Toni can be paid in one of two ways: Plan \(A:\) A salary of \(\$ 400\) per month, plus a commission of \(8 \%\) of gross sales; Plan \(B:\) A salary of \(\$ 610\) per month, plus a commission of \(5 \%\) of gross sales. For what amount of gross sales should Toni select plan A?

To prepare for Section 2.5, review translating to algebraic expressions and equations. Translate to an algebraic expression or equation. Erin is returning a tent that she bought during a \(25 \%\) off storewide sale that has ended. She is offered store credit for \(125 \%\) of what she paid (not to be used on sale items). Is this fair to Erin? Why or why not?

Use an inequality and the five-step process to solve each problem. Abriana rented a compact car for a business trip. At the time of the rental, she was given the option of prepaying for an entire tank of gasoline at \(\$ 3.099\) per gallon, or waiting until her return and paying \(\$ 6.34\) per gallon for enough gasoline to fill the tank. If the tank holds 14 gal, how many gallons can she use and still save money by choosing the second option?

Pam scored 78 on a test that had 4 fill in questions worth 7 points each and 24 multiplechoice questions worth 3 points each. She had one fill-in question wrong. How many multiple-choice questions did Pam get right?

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.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.