/*! 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 131 Solve the equation for the varia... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 131

Solve the equation for the variable. $$7 z=39-6 z$$

Short Answer

Expert verified
\(z = 3\)

Step by step solution

01

Isolate the variable term on one side

Add 6z to both sides of the equation to move the variable term to one side. The equation is then transformed as follows:\[ 7z + 6z = 39 - 6z + 6z \]This simplifies to:\[ 13z = 39 \]
02

Solve for the variable

Divide both sides of the equation by 13 to isolate the variable z. The equation becomes:\[ z = \frac{39}{13} \]This simplifies to:\[ z = 3 \]

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.

isolate the variable
When solving linear equations, one of the first steps is to isolate the variable. Essentially, this means getting the variable on one side of the equation by itself. This helps us to see more clearly what the variable equals. For example, in the equation provided: 7z = 39 - 6z, we want all the terms involving the variable z on one side. Add 6z to both sides to move all z terms to one side: \(7z + 6z = 39 - 6z + 6z\). After adding, we get \(13z = 39\). Now, the variable z is isolated on one side, making it easier to solve.
combine like terms
A crucial aspect of simplifying equations is to combine like terms. Like terms are terms that contain the same variable raised to the same power. Once we have moved all variable terms to one side of the equation, we combine them to simplify. In the given exercise, after isolating the variable terms, we have: \(7z + 6z = 39\). Notice both terms on the left side include z. Adding them together, we get: \(13z = 39\). This makes the equation simpler and easier to solve.
simplify the equation
The final step in solving the linear equation is to simplify it and solve for the variable. After isolating the variable and combining like terms, the equation becomes \(13z = 39\). To find the value of z, divide both sides by 13: \(z = \frac{39}{13}\). This simplification gives us: \(z = 3\). Simplifying every step of the equation helps in arriving at the correct answer in a systematic and easy-to-follow manner.

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 the following exercises, solve each equation by clearing the fractions. $$ \frac{1}{3} x+\frac{1}{5} x=8 $$

In the following exercises, solve each equation by clearing the fractions. $$ \frac{2}{5} n-\frac{1}{10}=\frac{7}{10} $$

In the following exercises, translate into an equation and solve. Connor鈥檚 temperature was 0.7 degrees higher this morning than it had been last night. His temperature this morning was 101.2 degrees. What was his temperature last night?

In the following exercises, solve each linear equation using the general strategy. $$ 9(2 p-5)=72 $$

In the following exercises, solve the equations with constants and variables on both sides. $$ 12 x-9=3 x+45 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

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.