/*! 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 30 Solve each equation. $$ -y+4... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 30

Solve each equation. $$ -y+4 y=33 $$

Short Answer

Expert verified
y = 11

Step by step solution

01

Simplify the Equation

First, we simplify the equation by combining like terms. The equation is \[-y + 4y = 33\].Combine \(-y\) and \(4y\) to get \(3y\). This simplifies the equation to \[3y = 33\].
02

Solve for y

To solve for \(y\), divide both sides of the equation by \(3\):\[ y = \frac{33}{3} \].This will give us \[ y = 11 \].

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
When we talk about solving equations, we mean finding the value of the variable that makes the equation true. Equations often contain unknowns or variables, like \(y\) in this case. The goal is to isolate the variable on one side of the equation, so its value can be clearly seen.
Steps to solve an equation typically involve reversing the order of operations (PEMDAS/BODMAS) through:
  • Elimination of any addition or subtraction.
  • Dealing with any multiplication or division.
To ensure accuracy, always work to balance both sides of the equation, as what is done to one side must be done to the other.
Here, our equation \(-y + 4y = 33\) involves variable terms that we need to process to find the value of \(y\).
Combining Like Terms
Combining like terms is an essential technique in algebra that helps simplify equations. Like terms are terms that have the same variable raised to the same power. They can be added or subtracted together straightforwardly.
For example, in the equation \(-y + 4y = 33\), both \(-y\) and \(4y\) are like terms because they contain the variable \(y\) to the first power. To combine them, simply add the coefficients (numbers in front of the variables).
Here are the steps you would typically follow:
  • Identify terms that have the same variable and power.
  • Add or subtract the coefficients.
  • Rewrite the equation with these combined terms, reducing complexity.
In this specific problem, combining \(-y\) and \(4y\) results in the new equation: \(3y = 33\). This makes it much easier to see how to proceed.
Division in Algebra
Division in algebra is a straightforward method used to isolate variables and solve equations. It involves dividing each term in the equation by a number to simplify or solve for the variable.
In our solved equation \(3y = 33\), we've already combined like terms, leaving us with a simple expression that we can divide. Here's how it works:
  • Identify the coefficient of the variable.
  • Divide both sides of the equation by this coefficient to solve for the variable.
  • Check the simplified result to ensure correctness.
For the equation \(3y = 33\), dividing both sides by \(3\) isolates \(y\), resulting in \(y = 11\). Division here is pivotal as it extracts \(y\) from its multiplied state, revealing its value clearly.

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

Perform the indicated operations. See Sections 1.5 and 1.6 $$ \frac{3}{4}-\frac{3}{16} $$

Fill in the blanks with numbers of your choice so that equation has the given solution. Note: Each blank may be replaced with a different number. \(x-\)_____=_____ ; Solution: \(-10\)

Solve each inequality. Graph the solution set and write it in interval notation. $$ 2 \leq 3 x-10 \leq 5 $$

At this writing, the women's world record for throwing a disc (like a heavy Frisbee) was set by Jennifer Griffin of the United States in \(2000 .\) Her throw was 138.56 meters, The men's world record was set by Christian Sandstrom of Sweden in 2002 . His throw was \(80.4 \%\) farther than Jennifer's. Find the distance of his throw. Round to the nearest meter. (Source: World Flying Disc Federation)

Place \(\leq,>,\) or \(=\) in the appropriate space to make each a true statement. See Sections \(1.2,1.4,\) and 1.7 $$ (-3)^{2}-3^{2} $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.