/*! 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 325 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 325

In the following exercises, solve the equation. Then check your solution. $$ x-5=-11 $$

Short Answer

Expert verified
The solution is \( x = -6 \). This satisfies the equation.

Step by step solution

01

Isolate the Variable

To solve for the variable, isolate it on one side of the equation. Since the equation is given as \( x - 5 = -11 \), you can add 5 to both sides to isolate \(x\).\( x - 5 + 5 = -11 + 5 \)
02

Simplify the Equation

Simplify both sides of the equation to find the value of \(x\). This will cancel out the -5 and +5 on the left side.\( x = -6 \)
03

Check Your Solution

Substitute \( x = -6 \) back into the original equation to verify if it satisfies the equation.Original equation: \( x - 5 = -11 \)Substitute \( x = -6 \): \( -6 - 5 = -11 \)Simplify: \( -11 = -11 \). Since both sides of the equation are equal, the solution is verified as correct.

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.

isolating variables
When solving a linear equation, the first step is usually to isolate the variable. In our example, the equation given is \( x - 5 = -11 \).
To isolate \( x \), we need to get rid of the -5 on the left side.
Add 5 to both sides of the equation: \( x - 5 + 5 = -11 + 5 \).
This operation simplifies the equation to \( x = -6 \).
Now, our variable \( x \) is isolated, and we can see its value clearly.
simplifying equations
Simplifying equations means reducing them to their most basic form. In the example, once we add 5 to both sides, we get \( x = -6 \).
This step involves performing basic arithmetic operations to reach a simpler form of the equation.
Typically, you'll be working with addition, subtraction, multiplication, or division to simplify.
Always ensure that you perform the same mathematical operation on both sides of an equation to maintain balance. This keeps the equation valid and leads you to the correct solution.
checking solutions
After solving for the variable, it is crucial to check if the solution is correct. In our case, we found that \( x = -6 \).
Substitute \( x = -6 \) back into the original equation \( x - 5 = -11 \):
-6 - 5 = -11
Since both sides of the equation are equal \( -11 = -11 \), the solution is verified as correct.
This step ensures that you didn't make any mistakes in the process and that your solution works perfectly for the given 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

Mollie had a 16 -ounce cappuccino at her neighborhood coffee shop. The cappuccino had 110 calories. If Mollie walks for one hour, she burns 246 calories. For how many minutes must Mollie walk to burn off the calories in the cappuccino? Explain your reasoning.

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places. Breakfast cereal, 18 ounces for \(\$ 3.99\) or 14 ounces for \(\$ 3.29\)

In the following exercises, translate the English phrase into an algebraic expression. the ratio of \(y\) and 5\(x\)

In the following exercises, find the unit rate. Round to two decimal places, if necessary. \(\$595 \text { for 40 hours }\)

Sales Tax Hyo Jin lives in San Diego. She bought a refrigerator for \(\$ 1624.99\) and when the clerk calculated the sales tax it came out to exactly \(\$ 142.186625\) Round the sales tax to the nearest (a) penny (b) dollar.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

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.