/*! 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 34 Solve. $$ 270+y=800 $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 34

Solve. $$ 270+y=800 $$

Short Answer

Expert verified
y = 530

Step by step solution

01

Isolate the variable y

To isolate the variable y, subtract 270 from both sides of the equation. This will help to move the constant term to the other side.
02

Perform the subtraction

After subtracting 270 from both sides, the equation becomes: 270 + y - 270 = 800 - 270 This simplifies to y = 530.
03

Write the final solution

Therefore, the value of y is 530.

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.

Isolating Variables
Isolating variables is a key step in solving linear equations. It means we rearrange the equation to have the unknown variable on one side by itself. In the example: $$ 270 + y = 800 $$, we want to find the value of y. We do this by moving the 270 to the other side of the equation. To move the 270, we use subtraction because the 270 is added to y.

We subtract 270 from both sides of the equation:
$$ 270 + y - 270 = 800 - 270 $$
After performing this operation, we get: $$ y = 530 $$
This tells us that y is isolated and its value is 530. Remember, isolating the variable makes it easy to see its value clearly.
Equation Simplification
Equation simplification helps to make equations easier to handle. It involves combining like terms and performing arithmetic operations to reduce the equation to a simpler form.

In our example, after isolating y, we subtract 270 from both sides which simplifies the equation:
$$ 270 + y - 270 = 800 - 270 $$
This results in: $$ y = 530 $$
Simplification often includes steps like:
  • Combining like terms (terms that have the same variables)
  • Performing arithmetic operations like addition, subtraction, multiplication, and division

By simplifying the equation, we have a clearer understanding of the relationship between the variables and constants.
Basic Algebra
Basic algebra consists of foundational principles like solving equations, understanding variables, and performing arithmetic operations. In our example:
$$ 270 + y = 800 $$
We use the principle that an equation states equivalence between two expressions. To maintain this equivalence, any operation done on one side must also be done on the other side.

Here are key basics applied in the example:
  • Variables: The letter 'y' represents an unknown value.
  • Constants: The numbers 270 and 800.
  • Operations: To isolate the variable, we subtract 270 from both sides.

Hence, solving gets simplified to basic arithmetic once the equation form is understood. Learning these principles will help you solve more complex problems in the future.

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 order to make money on loans, financial institutions must be paid back more money than they loan. Suppose you borrow \(\$ 120,000\) to buy a house and agree to make monthly payments of \(\$ 872.67\) for 15 years. How much do you pay back altogether? How much more do you pay back than the amount of the loan?

The water in a filled tank weighs \(748.45 \mathrm{lb}\). One cubic foot of water weighs \(62.5 \mathrm{lb}\). How many cubic feet of water does the tank hold?

You can drive from home to work using either of two routes: Route A: Via interstate highway, \(7.6 \mathrm{mi}\), with a speed limit of \(65 \mathrm{mph}\). Route \(B\) : Via a country road, \(5.6 \mathrm{mi}\), with a speed limit of \(50 \mathrm{mph}\). Assuming you drive at the posted speed limit, which route takes less time? (Use the formula distance \(=\) speed \(\times\) time. \()\)

Add. $$ 99.6001+7285.18+500.042+870 $$

One U.S. dollar was worth about 17.7178 Mexican pesos recently. Write a word name for 17.7178
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.