/*! 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 7 Solve each equation using the me... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 7

Solve each equation using the methods shown in this section. $$7 y-3=4 y-15$$

Short Answer

Expert verified
The solution to the equation is \( y = -4 \).

Step by step solution

01

Simplify by Combining Like Terms

To begin solving the equation, we want to combine like terms. We can see that both sides of the equation have terms with "y" in them. Let's first get all terms with "y" on the same side of the equation by subtracting \(4y\) from both sides.\[7y - 4y - 3 = 4y - 4y - 15\]This simplifies to:\[3y - 3 = -15\]
02

Isolate the Variable Term

Now, we need to isolate the term with the variable "y". To do this, add 3 to both sides of the equation:\[3y - 3 + 3 = -15 + 3\]This simplifies to:\[3y = -12\]
03

Solve for the Variable

Finally, we want to solve for the variable "y" by dividing each side of the equation by 3:\[\frac{3y}{3} = \frac{-12}{3}\]This results in:\[y = -4\]

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.

Combining Like Terms
When solving linear equations, the first step often involves combining like terms. Like terms are simply terms that contain the same variable raised to the same power. For example, terms with "y," like "7y" and "4y," are like terms because they both include "y" to the power of one.
To combine them, you can simply add or subtract their coefficients. A coefficient is the number that is multiplying the variable. In this case, you have "7y" and "4y." Subtracting these gives you "3y," effectively reducing the equation's complexity.
  • This is done to make the equation easier to solve.
  • It simplifies the equation, allowing you to see the real relationships between numbers and variables.
  • We also move one term across the equation so like terms appear on the same side, making subtraction possible.
By combining like terms, you take a crucial step towards simplifying and ultimately solving the equation.
Isolating Variable
The goal of solving a linear equation is to find the value of the variable. This is reached through a process called isolating the variable. Once like terms have been combined, it's time to isolate the variable term to one side of the equation while keeping the numbers (constants) on the other.
To achieve this, you need to add or subtract terms from both sides of the equation. In our case, we add 3 to both sides, since we had "3y - 3 = -15."
  • By adding 3 to both sides, the "-3" on the left cancels out.
  • This leaves you with just "3y" on one side and "-12" on the other.
  • Remember, whatever you do to one side of the equation, do to the other; this keeps the equation balanced.
Through this step, "3y" is left alone on one side, perfectly setting up the next phase of solving for "y."
Dividing Coefficients
After isolating the variable term, you may end up with a coefficient in front of the variable. To find the variable's actual value, you need to divide both sides by this coefficient. Here, the coefficient next to "y" is 3, resulting in the equation "3y = -12."
Divide everything by 3 to remove the coefficient from the variable "y."
  • This step involves dividing both sides of the equation by 3.
  • On the left, \(\frac{3y}{3}\), simplifies to "y."
  • On the right, \(\frac{-12}{3}\), becomes "-4."
Thus, you find that "y" equals "-4." This shows you've successfully solved for the variable, accurately completing this linear equation.

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

Simplify each expression. $$\left(\frac{13}{21}-\frac{13}{35}\right)^{2}$$

Multiply. $$\left(-\frac{5}{4}\right)\left(-\frac{4}{5}\right)$$

Perform the indicated operation. $$\frac{3}{5}-\frac{5}{8}$$

Multiply. $$\frac{1}{4} \cdot 4$$

Find the complement and supplement of each angle. [Example \(6]\) $$59^{\circ}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Geometry

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.