/*! 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 18 Solve and check. $$3 y-9=0$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 18

Solve and check. $$3 y-9=0$$

Short Answer

Expert verified
The solution is \( y = 3 \)

Step by step solution

01

Isolate the y term

The first step toward solving this problem is to isolate the \( y \) term. This is done by adding 9 to both sides of the equation, which gives us: \( 3y = 9 \)
02

Divide by coefficient of y

Next, we will divide both sides by 3 (the coefficient of y). This gives us the solution: \( y = 9/3 = 3 \)
03

Check the Solution

To ensure our solution is correct, we'll substitute \( y = 3 \) back into the original equation. 3 * 3 - 9 = 9 - 9 = 0, which is true. This verifies that \( y = 3 \) is indeed the correct solution.

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.

Isolation of Variables
When solving linear equations, one of the primary steps is the isolation of the variable. In our exercise, the goal is to solve for \( y \) in the equation \( 3y - 9 = 0 \). Isolation means we want \( y \) to stand by itself on one side of the equation.To begin isolating \( y \), we need to undo any operations that are being applied to it. Here, \( y \) is first multiplied by 3 and then 9 is subtracted from the result. To isolate \( y \), we perform operations that reverse these effects:
  • First, add 9 to both sides of the equation to neutralize the -9. This step changes the equation to \( 3y = 9 \).
  • Next, to further isolate \( y \), we will need to tackle the multiplication by 3.
Isolating variables is critical because it helps reveal the "pure" value of the variable we're solving for, without any distractions from other numbers or operations.
Checking Solutions
Once you have found a potential solution for a linear equation, it's essential to verify that the solution actually fits the original equation. This is known as checking solutions.For our exercise, we found that \( y = 3 \) was the solution. To check if this is correct, substitute \( y = 3 \) back into the original equation, \( 3y - 9 = 0 \). Performing these calculations gives us:
  • \( 3 \times 3 - 9 = 9 - 9 = 0 \)
The left side of the equation is zero, which matches the right side, confirming our solution. Checking solutions helps ensure accuracy and correctness, preventing mistakes and providing peace of mind that the solution is solid.
Coefficient of a Variable
In the context of linear equations, the coefficient of a variable is the number that is multiplied by the variable. Understanding this concept is pivotal when solving equations as it informs the steps needed to isolate the variable.In our exercise equation \( 3y - 9 = 0 \), the coefficient of the variable \( y \) is 3. This coefficient tells us how many "units" of \( y \) are present. When isolating \( y \), it is necessary to remove this coefficient by dividing both sides of the equation by 3:
  • This step gives the solution: \( y = 3 \).
Recognizing and properly handling coefficients is crucial, as it effectively leads to simplified and correct solutions to the equations.

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

Solve. $$ \frac{4}{\frac{3}{b}}=8 $$

As part of a training program for the Boston Marathon, a runner wants to build endurance by running at a rate of 9 mph for 20 min. How far will the runner travel in that time period?

Solve and check. $$7 d-4 d=9$$

The Ride for Health Bicycle Club has chosen a 36 -mile course for this Saturday's ride. If the riders plan on averaging 12 mph while they are riding, and they have a 1-hour lunch break planned, how long will it take them to complete the trip?

Solve and check. $$-\frac{1}{6} n=-30$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.