/*! 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 44 Solve each equation. Be sure to ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 44

Solve each equation. Be sure to check each result. $$ \frac{2 m}{9}=4 $$

Short Answer

Expert verified
The solution is \( m = 18 \).

Step by step solution

01

Isolate the Variable

To solve the equation \( \frac{2m}{9} = 4 \), start by isolating \( m \) on one side of the equation. Multiply both sides of the equation by 9 to eliminate the fraction. This gives:\[ 2m = 36\]
02

Solve for the Variable

Next, solve for \( m \) by dividing both sides of the equation by 2:\[m = \frac{36}{2}\]Simplifying the right side, you get:\[m = 18\]
03

Verify the Solution

To ensure the solution is correct, substitute \( m = 18 \) back into the original equation:\[\frac{2(18)}{9} = 4\]Simplify the left-hand side:\[\frac{36}{9} = 4\]Which confirms:\[4 = 4\]Thus, the solution \( m = 18 \) 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.

Isolating Variables
One of the first steps in solving linear equations is isolating the variable, which means getting the variable of interest by itself on one side of the equation. This involves reversing the operations that are being performed on the variable. Think of it as peeling back layers to reveal what's underneath, which, in this case, is the variable itself.
To isolate a variable:
  • Identify the operations applied to the variable.
  • Perform inverse operations to undo these operations.
  • Whatever you do to one side of the equation, you must do to the other side to maintain equality.
In our example, the goal was to isolate \( m \) in the fraction \( \frac{2m}{9} = 4 \). We multiplied both sides by 9 to remove the fraction, leaving us with \( 2m = 36 \). This step is crucial because it simplifies the equation into a form that's easier to solve.
Fractions in Equations
Dealing with fractions in equations can be intimidating, but it doesn't have to be. When fractions are involved, a common technique is to eliminate the fractions by multiplying both sides of the equation by a common denominator. This transforms the problem into a simpler, fraction-free equation.
The process of removing fractions:
  • Identify the denominator in the fraction.
  • Multiply both sides of the equation by this denominator to clear the fraction.
  • Simplify the resulting equation.
In the equation \( \frac{2m}{9} = 4 \), multiplying both sides by 9 effectively cleared the fraction, making it much easier to continue solving for \( m \). Now with \( 2m = 36 \), we have a fraction-free equation that's straightforward to tackle.
Checking Solutions
Always check your solutions to ensure accuracy and understanding. Verifying the solution involves substituting your calculated value back into the original equation and ensuring the equality holds true. This step confirms that you have not made a mistake and reinforces your confidence in the solution.
How to check your solution:
  • Take the solution you've found and substitute it back into the original equation.
  • Simplify both sides of the equation to check if they are equal.
  • If they are, your solution is verified.
In this case, substituting \( m = 18 \) back into the original equation \( \frac{2(18)}{9} = 4 \) simplifies to \( \frac{36}{9} = 4 \), proving that \( 4 = 4 \). This confirms the solution \( m = 18 \) is indeed correct.

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

Translate each phrase or sentence to a mathematical expression or equation. Eleven added to three times a number.

Translate each phrase or sentence to a mathematical expression or equation. Three fifths of a number plus eight is fifty.

For problems \(57-140\), solve each equation. $$ \frac{5 x}{-2}-6=-10 $$

Solve the equation \(\frac{3 x}{4}+1=-5\)

For problems \(57-140\), solve each equation. $$ 3=4 a-2 a+a $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.