/*! 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 14 Solve each equation. $$ \sqr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 14

Solve each equation. $$ \sqrt{5 x+1}-11=0 $$

Short Answer

Expert verified
The solution is \(x = 24\).

Step by step solution

01

Isolate the Square Root Term

Move all other terms to the right-hand side of the equation. \(\sqrt{5x + 1} = 11\)
02

Square Both Sides

Eliminate the square root by squaring both sides of the equation.\((\sqrt{5x + 1})^2 = 11^2\)This simplifies to\(5x + 1 = 121\)
03

Solve for x

Isolate x by subtracting 1 from both sides and then dividing by 5.\(5x = 120\)Divide both sides by 5.\(x = 24\)

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 Terms
When solving a square root equation, your first task is to isolate the square root term. This means separating the part of the equation containing the square root from all other elements. For instance, in the equation \(\sqrt{5x+1} - 11 = 0\), you want to move the '-11' to the other side of the equation.
To achieve this, we'll add '11' to both sides:
\(\sqrt{5x+1} = 11\)
Now the square root term is isolated on one side of the equation.
Square Both Sides
Once you have isolated the square root term, the next step involves eliminating the square root symbol. You do this by squaring both sides of the equation. For example:
\[(\sqrt{5x + 1})^2 = 11^2\]
When you square a square root, you are left with the term inside the square root. Hence, the equation now becomes:
\[5x + 1 = 121\]
This step is crucial because it transforms a potentially complex problem into a simpler, linear equation.
Algebraic Manipulation
At this stage, you need to use basic algebraic operations to further simplify the equation. In our example, the equation is:
\(5x + 1 = 121\)
First, isolate the term containing the variable 'x' by subtracting '1' from both sides:
\(5x = 120\)
These simple operations continue to simplify the equation, bringing you one step closer to finding the value of 'x'.
Solve for x
The final step is to solve for the variable 'x'. Once you have simplified your equation to the form \(5x = 120\), the last operation is to isolate 'x'. You do this by dividing both sides by the coefficient of 'x', in this case, '5':
\(x = \frac{120}{5}\)
Perform the division to find:
\(x = 24\)
So, the solution to the equation \(\sqrt{5x + 1} - 11 = 0\) is \(x = 24\). Using these concepts step by step will simplify solving square root equations.

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. Assume that all variables represent positive real numbers. \(\sqrt[3]{-16 z^{5} t^{7}}\)

Simplify. Assume that all variables represent positive real numbers. \(-\sqrt[3]{64 y^{18}}\)

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \sqrt{\sqrt[3]{\sqrt[4]{x}}} $$

Write each radical as an exponential and simplify. Leave answers in exponential form. Assume that all variables represent positive numbers. $$ \sqrt{y} \cdot \sqrt[3]{y z} $$

List all of the following sets to which each number belongs. A number may belong to more than one set. real numbers pure imaginary numbers nonreal complex numbers complex numbers $$ -7 i $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.