/*! 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 34 For exercises 1-72, (a) solve.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 34

For exercises 1-72, (a) solve. (b) check. $$ 9-m=27 $$

Short Answer

Expert verified
\(m = -18\)

Step by step solution

01

- Isolate the Variable

To solve for the variable, subtract 9 from both sides of the equation. This will isolate the variable on one side.\(9 - m - 9 = 27 - 9\)Thus, we have:\(-m = 18\)
02

- Solve for the Variable

Since \(-m = 18\), multiply both sides by -1 to solve for \(m\).\(-1 \times -m = -1 \times 18\)Thus, \(m = -18\).
03

- Check the Solution

Substitute \(m = -18\) back into the original equation to verify the solution.\(9 - (-18) = 27\)This simplifies to:\(9 + 18 = 27\)And indeed, \(27 = 27\), which confirms that our solution is 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.

Isolate the Variable
To solve linear equations, the first key step is to isolate the variable. This means getting the variable by itself on one side of the equation.
In the example given \(9 - m = 27\), our goal is to isolate \(m\).
We achieve this by using inverse operations. Here, we subtract 9 from both sides of the equation:
\(9 - m - 9 = 27 - 9\).
This gives us \(-m = 18\).
By isolating the variable, we simplify the equation and get closer to finding the solution.
Checking Solutions
After solving an equation, it's important to verify that our solution is correct. This is known as checking solutions.
We do this by substituting the value of the variable back into the original equation.
In our example, we determined that \(m = -18\). To check if this is correct, substitute \(m\) with \(-18\) in the original equation:
\(9 - (-18) = 27\).
Since \(9 + 18 = 27\) simplifies to \(27 = 27\), we see that the left-hand side equals the right-hand side, confirming that our solution is indeed correct.
Inverse Operations
Inverse operations are fundamental tools for solving linear equations. They help us isolate the variable by reversing the operations presented in the equation.
Common inverse operations include:
  • Addition and subtraction
  • Multiplication and division
For example, if an equation involves subtraction, we use addition to cancel it out, and vice versa.
In our exercise, \(9-m=27\), we use subtraction (the inverse of addition) to isolate \(m\).
Once we had \(-m = 18\), we used multiplication by \(-1\) (the inverse of -1 multiplication) to solve for \(m\).
Understanding and using inverse operations efficiently is crucial for solving any linear 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

For exercises \(65-72\), assign a variable, and write an inequality that represents the constraint. The number of ballots affected by a technical problem in mailing A technical problem was affecting the mailing of up to 21,000 ballots. (Source: www.seattletimes.com, Nov. 7, 2011)

Each of the four sides of a square is the same length. If \(P\) is the perimeter of the square and \(S\) is the length of a side, write a formula in \(P\) and \(S\) for the perimeter of a square and solve this formula for \(S\).

Solve: \(7(2 c-1)=15(c-3)-c\)

For exercises 53-62, (a) clear the fractions or decimals and solve. (b) check the direction of the inequality sign. $$ \frac{1}{4} m+\frac{1}{6}>1 $$

Describe the difference between the properties of equality and the properties of inequality.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.