/*! 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 69 Solve the proportions. $$\frac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 69

Solve the proportions. $$\frac{x+3}{x}=\frac{5}{4}$$

Short Answer

Expert verified
x = 12

Step by step solution

01

- Set up the equation

Start by writing the proportion equation: \[ \frac{x+3}{x} = \frac{5}{4} \]
02

- Cross-multiply to eliminate the fraction

Cross-multiplying the two fractions will help eliminate the denominators: \[ 4(x+3) = 5x \]
03

- Expand the equation

Expand the left side of the equation: \[ 4x + 12 = 5x \]
04

- Isolate the variable

Subtract 4x from both sides of the equation to isolate the variable: \[ 12 = 5x - 4x \] \[ 12 = x \]
05

- Verify the solution

Substitute x = 12 back into the original equation to ensure the solution is correct: \[ \frac{12 + 3}{12} = \frac{15}{12} = \frac{5}{4} \], which confirms the solution.

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 method used to eliminate the fractions in an equation by multiplying the numerator of each fraction by the denominator of the other fraction. In our exercise, we have the proportion \[ \frac{x+3}{x} = \frac{5}{4} \]. To start, we cross-multiply the two fractions. This means multiplying the left numerator (\(x+3\)) by the right denominator (4) and the left denominator (x) by the right numerator (5). The result is: \[ 4(x+3) = 5x \]. This step helps us to remove the fractions and simplifies the process of solving for x.
Isolating Variables
Next, we need to isolate the variable x to solve the equation. After cross-multiplication, our equation is \[ 4(x+3) = 5x \], which expands to \[ 4x + 12 = 5x \]. To isolate x, we subtract 4x from both sides: \[ 4x + 12 - 4x = 5x - 4x \]. This simplifies to \[ 12 = x \]. By moving all terms with the variable to one side and the constants to the other, we effectively isolate x, making it easy to see that x equals 12. This step is crucial in solving equations as it allows us to determine the value of the unknown variable.
Verification of Solutions
After solving for the variable, it鈥檚 important to verify our solution to ensure it is correct. We do this by substituting the value of x back into the original equation. For our example, substituting x = 12 gives us: \[ \frac{12+3}{12} = \frac{15}{12} = \frac{5}{4} \]. Since the left-hand side equals the right-hand side of the original proportion, our solution is verified. Verification is an essential step as it confirms that the solutions are accurate and the equation balances correctly.

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

Define the key terms. a. Rate b. Unit rate c. Unit cost

To measure the height of the Washington Monument, a student \(5.5 \mathrm{ft}\) tall measures his shadow to be \(3.25 \mathrm{ft}\). At the same time of day, he measured the shadow of the Washington Monument to be \(328 \mathrm{ft}\) long. Estimate the height of the monument to the nearest foot.

Write each rate in lowest terms. There are 130 calories in 8 snack crackers.

Write the ratio in two other ways. $$8: 13$$

A window is \(2 \mathrm{ft}\) wide and 3 yd in length \(\left(2 \mathrm{ft} \text { is } \frac{2}{3} \mathrm{yd}\right)\) (PICTURE NOT COPY) A. Find the ratio of width to length with all units in yards. B. Find the ratio of width to length with all units in feet.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.