/*! 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 11 Solve each proportion for the va... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 11

Solve each proportion for the variable. \(\frac{x}{8}=\frac{6}{24}\)

Short Answer

Expert verified
The value of \( x \) is 2.

Step by step solution

01

Cross Multiply

To solve the proportion \( \frac{x}{8} = \frac{6}{24} \), use the cross multiplication method. Multiply the numerator of one fraction by the denominator of the other: \( x \times 24 \) and \( 6 \times 8 \). This gives the equation \( 24x = 48 \).
02

Solve for x

Next, isolate \( x \) by dividing both sides of the equation by 24: \( \frac{24x}{24} = \frac{48}{24} \). This simplifies to \( x = 2 \).
03

Verify the Solution

To ensure the solution is correct, substitute \( x = 2 \) back into the original proportion: \( \frac{2}{8} = \frac{6}{24} \). Simplifying both sides, we have \( \frac{1}{4} = \frac{1}{4} \), which confirms the 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.

Cross Multiplication
Cross multiplication is a technique used to solve proportions like \( \frac{x}{8} = \frac{6}{24} \). It involves multiplying diagonally across the equal sign to simplify the problem. Here鈥檚 how it works: you multiply the numerator (top number) of one fraction by the denominator (bottom number) of the other fraction. This creates an equation without fractions, often making it easier to solve. In this case:
  • Multiply \( x \) (numerator on the left) by 24 (denominator on the right): \( x \times 24 \).
  • Multiply 6 (numerator on the right) by 8 (denominator on the left): \( 6 \times 8 \).
This results in the equation \( 24x = 48 \), a key step in solving the proportion. By removing fractions, cross multiplication helps in focusing on the core numerical values, streamlining the solving process.
Equation Solving
Equation solving is the process of finding the unknown variable that satisfies the equation. After establishing the cross-multiplying equation \( 24x = 48 \), the next step is to isolate the variable, \( x \). This typically involves performing inverse operations to both sides of the equation to keep it balanced. Here鈥檚 how it proceeds:
  • Divide every term by 24 to isolate \( x \): \( \frac{24x}{24} = \frac{48}{24} \).
  • Simplify the right side: \( x = 2 \).
Through division, we effectively turn the complex part of the equation into a simpler statement. It showcases the power of inverse operations, where dividing by a number counteracts multiplication. This balance leads you directly to the solution, \( x = 2 \), showing the elegance and practicality of mathematical reasoning.
Verification of Solution
Verification of solution is a critical step to ensure the accuracy of your work. Once we found the answer \( x = 2 \), we must check if it holds true in the original equation \( \frac{x}{8} = \frac{6}{24} \). Here's how you can verify:
  • Substitute \( x = 2 \) back into the original proportion: \( \frac{2}{8} \).
  • Simplify both sides of the equation to confirm equality.
  • The left-hand side simplifies to \( \frac{1}{4} \).
  • The right-hand side, \( \frac{6}{24} \), also simplifies to \( \frac{1}{4} \).
Both sides equal \( \frac{1}{4} \), proving that \( x = 2 \) is indeed the correct solution. This step not only reassures the correctness of our solution but also builds confidence in our ability to carry out precise calculations. Verifying solutions is a must, especially in complex problems.

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

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{2 x^{2}+1}{5 x}-\frac{7 x^{2}-1}{5 x} $$

In \(3-20,\) solve each equation and check. $$ \frac{x}{5}-\frac{x}{10}=7 $$

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{1}{x}+\frac{1}{x-2}-\frac{2}{x^{2}-2 x} $$

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ 5-\frac{1}{2 y} $$

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{b}{b-1}-\frac{1}{2-2 b} $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Pure 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.