/*! 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 Determine whether the given numb... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 44

Determine whether the given number is a solution of the equation. $$\frac{x}{7}=7 x ; 0$$

Short Answer

Expert verified
Yes, the given number (0) is a solution to the equation.

Step by step solution

01

Substitute the given number

Replace the variable x in the equation with the given number. Here, the given number is 0. So, the equation will be \(\frac{0}{7} = 7*0\)
02

Simplify the equation

Next, simplify both sides of the equation. The left side simplifies to 0, and the right side also simplifies to 0.
03

Verify the equality

The final step is to see if the simplified left side is equal to the simplified right side. If they are equal, then the number is a solution to the equation. Since both sides of the equation are 0, the given number, 0, is indeed a solution to the given equation

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.

Understanding Equations
An equation is a mathematical statement that asserts the equality of two expressions. In simpler terms, it's like a math sentence using an equal sign. Equations are fundamental in algebra and involve numbers, variables, and operations. For example, the equation \( \frac{x}{7} = 7x \) is saying that whatever value \( x \) is, dividing it by 7 will be the same as multiplying it by 7. This often requires finding a number that makes the equation true, which is what we call a solution.
Finding Solutions to Equations
The solution of an equation is a value of the variable that makes the equation true. In algebra, finding the solution means determining what number we can replace the variable with to satisfy the equation. For the equation \( \frac{x}{7} = 7x \), our task is to find what makes both sides equal. A solution is not just any number; it is the number that when substituted into the equation makes both sides equal each other precisely.
  • Solve or take steps to confirm if a number is a solution.
  • Substitute the number into the equation to see if it works.
In this case, replacing \( x \) with 0 shows that both sides equal 0, confirming 0 as a solution.
Substituting Variables
Variable substitution is a key step when solving equations. This involves replacing the variable or letter in an equation with a given number. This step helps check if that particular number is a solution of the equation. In our example, we substitute \( x = 0 \) into the equation \( \frac{x}{7} = 7x \). After substitution, the equation simplifies to \( \frac{0}{7} = 7 imes 0 \), making it easier to verify.
  • Replace the variable with the given number.
  • Rewrite the equation using the new number instead of the variable.
It simplifies the equation and helps to easily check if the number is a solution.
The Simplification Process
Simplification in algebra means reducing an equation to its simplest form. This involves performing the necessary arithmetic operations until the equation is more manageable. In our given problem, simplification makes it clear if the equation has been solved properly. For \( \frac{0}{7} = 7 imes 0 \), simplify each side:
  • Left side: \( \frac{0}{7} = 0 \) because dividing zero by any number is always zero.
  • Right side: \( 7 \times 0 = 0 \), as multiplying any number by zero results in zero.
After simplification, both sides are equal to zero, confirming that the substitution was correct and that 0 is a solution.

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

Explain the use of parentheses and brackets in the graphing of the solution of an inequality.

The perimeter of an equilateral triangle is at most 57 feet. What could be the length of a side? (Hint: All three sides of an equilateral triangle are equal.)

Explain why multiplying both sides of an inequality by a negative constant reverses the direction of the inequality.

A shopkeeper sells chocolate coffee beans for \(7\)dollar per pound. A customer asks the shopkeeper to mix 2 pounds of chocolate beans with 5 pounds of hazelnut coffee beans. If the customer paid \(6\)dollar per pound for the mixture, what is the price per pound of the hazelnut beans?

Solve each inequality and graph the solution on the number line. $$9 < -3 x < 15$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.