/*! 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 106 Solve \(y-3=-2(x-3)\) for \(y\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 106

Solve \(y-3=-2(x-3)\) for \(y\)

Short Answer

Expert verified
The solution for \(y\) is \(y = -2x + 9\).

Step by step solution

01

Distribute -2

The equation should be rewritten, distributing the -2 to both terms in the parenthesis. This yields: \(y - 3 = -2x + 6\).
02

Isolate y

Now, 'y' should be isolated by adding 3 to both sides of the equation. The solution is: \(y = -2x + 9\)

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.

Equation Solving
Equation solving is the process of finding the value of the variable that makes the equation true. In this exercise, our task is to solve for the variable \(y\) in the equation \(y - 3 = -2(x - 3)\). This means finding the expression for \(y\) in terms of \(x\).
When solving equations, you typically follow a sequence of logical steps:
  • Simplify both sides of the equation.
  • Perform operations like addition, subtraction, multiplication, or division to isolate the variable.
  • Verify your solution by substituting it back into the original equation to check for correctness.
Recognizing which operations or properties to use is key in equation solving, and involves understanding the specifics of each equation's structure.
Distributive Property
The distributive property is a fundamental mathematical principle used when dealing with parentheses in equations. It tells us to multiply each term inside the parentheses by the factor outside. In the equation \(y - 3 = -2(x - 3)\), we apply the distributive property to simplify the equation.
Here's how it works in this step:
  • Multiply \(-2\) by each term inside the parentheses.
  • This means we calculate \(-2 \times x\) and \(-2 \times -3\).
After performing these calculations, the equation \(y - 3 = -2x + 6\) is obtained.
The distributive property is essential in simplifying equations and is often one of the first steps in making the equation easier to solve. Learning to identify when and how to apply it allows for smoother problem-solving in mathematics.
Isolating Variables
Isolating the variable is the process of rearranging the equation so that the variable appears alone on one side, and here's how it can be done. In our exercise, the goal after applying the distributive property is to isolate \(y\).
To isolate \(y\) in the equation \(y - 3 = -2x + 6\), you:
  • Identify the terms that need to be moved to the other side of the equation.
  • Add 3 to both sides to cancel out the \(-3\) with \(+3\).
This gives us: \(y = -2x + 9\).
By isolating variables, we can solve equations and express one variable in terms of the other. This technique is fundamental and appears frequently in algebra, making it a core skill to master in any mathematics journey.

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 interval notation to express the solution set of each inequality. $$|2 x-1|>4$$

Solve by completing the square or by using the quadratic formula. $$\sqrt{2} x^{2}+3 x+\sqrt{2}-0$$

A sales clerk has a choice between two payment plans. Plan A pays \(\$ 100.00\) a week plus \(\$ 8.00\) a sale. Plan B pays \(\$ 250.00\) a week plus \(\$ 3.50\) a sale. How many sales per week must be made for plan A to yield the greater paycheck?

The notation \(\left.f(x)\right|_{a} ^{b}\) is used to denote the difference \(f(b)-f(a) .\) That is, $$\left.f(x)\right|_{a} ^{b}=f(b)-f(a)$$ Evaluate \(\left.f(x)\right|_{0} ^{b}\) for the given function \(f\) and the indicated values of \(a\) and \(b\). $$f(x)=-3 x+2 ;\left.f(x)\right|_{4} ^{7}$$

If \(g(x)=-2 x^{2}+4 x-1\) and \(g(c)=-4,\) find \(c\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

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.