/*! 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 10 Solve each equation. $$ \sqr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 10

Solve each equation. $$ \sqrt{7 x-3}=6 $$

Short Answer

Expert verified
x = \frac{39}{7}

Step by step solution

01

- Isolate the square root

The equation is given as \( \sqrt{7x - 3} = 6 \). We can see that the square root is already isolated.
02

- Square both sides

To eliminate the square root, square both sides of the equation: \[ (\sqrt{7x - 3})^2 = 6^2 \] Simplifying this, we get \[ 7x - 3 = 36 \]
03

- Solve for x

Now, solve for \(x\): Add 3 to both sides \[ 7x - 3 + 3 = 36 + 3 \] which simplifies to \[ 7x = 39 \] Finally, divide both sides by 7 \[ x = \frac{39}{7} \]

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 of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 times 3 is 9. In equations, the square root is often represented by the radical symbol (鈭�). So, the expression \( \sqrt{7x - 3} \) implies finding a value that when squared results in \( 7x - 3 \). Understanding this concept is vital because solving square root equations often involves reversing the square root operation.
algebraic equations
Algebraic equations are mathematical statements that assert the equality of two expressions. An equation consists of variables and constants combined using algebraic operations like addition, subtraction, multiplication, and division. In the exercise, \( \sqrt{7x - 3} = 6 \), the variable is \( x \), and the goal is to find its value. Solving algebraic equations often requires a sequence of operations to isolate the variable on one side of the equation.
isolating variables
Isolating the variable means manipulating the equation to get the variable alone on one side. This usually involves performing inverse operations. For the exercise \( \sqrt{7x - 3} = 6 \), the square root is already isolated, meaning our variable term \( 7x - 3 \) is under the square root and on one side of the equation. This is a crucial step before squaring both sides to solve for \( x \).
squaring both sides
Squaring both sides of an equation is an operation used to eliminate the square root. In the given problem, we squared both sides of \( \sqrt{7x - 3} = 6 \) to get \( 7x - 3 = 36 \). Squaring removes the square root because the square of a square root is the radicand (the number under the square root). Remember, whatever you do to one side of the equation, you must do to the other to maintain the equality.

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

Brain Busters Rationalize each denominator. Assume that all radicals represent real numbers and no denominators are 0. $$ \frac{q}{\sqrt{5+q}} $$

Solve each equation. $$ 5 x^{2}-3 x=2 $$

Fill in the blank with the correct response: Because \((4+2 i)-(3+i)=1+i,\) using the definition of subtraction, we can check this to find that \((1+i)+(3+i)=\) ________.

Simplify each radical. $$ \frac{2}{4+\sqrt{3}} $$

Find each quotient. $$ \frac{-1+5 i}{3+2 i} $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

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.