Problem 399 In the following exercises, solv... [FREE SOLUTION]

Chapter 9: Problem 399

In the following exercises, solve. \(\sqrt{6 v-2}-10=0\)

Short Answer

Expert verified

\(v = 17\)

Step by step solution

Isolate the square root

Add 10 to both sides of the equation to isolate the square root term: o \(\sqrt{6v - 2} - 10 = 0 \)o becomes o \(\sqrt{6v - 2} = 10 \)..

Square both sides

Square both sides of the equation to remove the square root: o \((\sqrt{6v - 2})^2 = 10^2 \)o becomes o \(6v - 2 = 100 \)..

Solve for v

Add 2 to both sides of the equation to isolate the term containing v: o \(6v - 2 + 2 = 100 + 2 \)o becomes o \(6v = 102 \).Finally, divide by 6 to solve for v: o \(v = \frac{102}{6} \)o which simplifies to o \(v = 17 \)..

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.

square root

The square root is a mathematical function that, when applied to a number, returns the value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 * 5 = 25. Notating square roots in math is typically done using the radical symbol \(\backslashsqrt{}\). When solving equations involving square roots, it is crucial to isolate the square root term to simplify the process.

isolating variables

Isolating variables means manipulating an equation so the variable of interest stands alone on one side. This often involves a series of algebraic steps such as addition, subtraction, multiplication, or division. For example, in the equation \(\backslashsqrt{6v - 2} - 10 = 0\), we add 10 to both sides to start isolating the variable: \(\backslashsqrt{6v - 2} = 10\). By performing inverse operations, we simplify the equation step by step until the variable is by itself.

squaring both sides

Squaring both sides of an equation is a method used to eliminate a square root. When dealing with square roots, it is often essential to square both sides to transform the equation into a simpler form. For instance, if you have \(\backslashsqrt{6v - 2} = 10\), squaring both sides gives \(( \backslashsqrt{6v - 2})^2 = 10^2\). This simplifies to \(6v - 2 = 100\), making it easier to solve for the variable.

addition and division in equations

Addition and division are core techniques in solving equations. For instance, after squaring both sides of \(\backslashsqrt{6v - 2} = 10\) to get \(6v - 2 = 100\), we need to use addition and division to isolate and solve for v. First, add 2 to both sides: \(6v - 2 + 2 = 100 + 2\) or simply, \(6v = 102\). Then, divide by 6: \(v = \backslashfrac{102}{6}\), which simplifies to \(v = 17\). Each step helps in methodically breaking down the problem to find the solution.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercises, solve. \(\sqrt{6 v-2}-10=0\)

Short Answer

Step by step solution

Isolate the square root

Square both sides

Solve for v

Key Concepts

square root

isolating variables

squaring both sides

addition and division in equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Geometry

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.