/*! 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 55 Solve using the multiplication p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 55

Solve using the multiplication principle. Don't forget to check! $$ \frac{4}{5} x=16 $$

Short Answer

Expert verified
The solution is x = 20.

Step by step solution

01

Identify the equation

The given equation is \(\frac{4}{5} x = 16\).
02

Isolate the variable (x)

To isolate x, multiply both sides of the equation by the reciprocal of \(\frac{4}{5}\). The reciprocal of \(\frac{4}{5}\) is \(\frac{5}{4}\). Thus, multiply both sides by \(\frac{5}{4}\) to get: \[ \left( \frac{5}{4} \right) \left( \frac{4}{5} x \right) = 16 \left( \frac{5}{4} \right) \]
03

Simplify the equation

Simplify the left side, \[ x = 16 \left( \frac{5}{4} \right) = 16 \cdot \frac{5}{4} = 16 \cdot 1.25 = 20 \]
04

Check the solution

Substitute the value of x back into the original equation to verify: \[ \frac{4}{5} \cdot 20 = 16 \] Simplify the left side, \[ 16 = 16 \] Since both sides are equal, 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.

Introduction to Algebra
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. It's all about finding the unknown in an equation. In this case, our unknown is the variable **x**. Equations often involve simple operations such as addition, subtraction, multiplication, or division. Here, we鈥檒l be focusing on solving an equation using multiplication. Keep in mind that we always aim to isolate the variable to determine its value.
Isolating Variables
The core of solving equations is isolating the variable. Isolating the variable means getting the variable alone on one side of the equation. Let's examine our problem: \(\frac{4}{5} x = 16\). The goal is to solve for **x**. To isolate **x**, you need to get rid of any constants or coefficients that are with it. This usually involves using inverse operations. In this case, we have the fraction \(\frac{4}{5}\) as a coefficient of **x**.
Using Reciprocal Multiplication
Reciprocal multiplication is the key to isolating variables in equations involving fractions. A reciprocal of a fraction is simply flipping the numerator and the denominator. So, the reciprocal of \(\frac{4}{5}\) is \(\frac{5}{4}\). When we multiply \(\frac{4}{5}\) by \(\frac{5}{4}\), we get 1 (since moving to the reciprocal undoes the fraction). To isolate **x**, multiply both sides of the equation by \(\frac{5}{4}\): \(\frac{5}{4} \times \frac{4}{5} x = 16 \times \frac{5}{4}\), simplifying to **x = 20**. Now, **x** is by itself on the left side.
Equation Verification
Verifying your solution is an essential step to make sure your solution is correct. Let's take our derived value **x = 20** and put it back into the original equation: \(\frac{4}{5} \times 20 = 16\). First, perform the multiplication on the left side: \(\frac{4}{5} \times 20 = 16\). Simplify the multiplication term to get \(\frac{80}{5} = 16\). Since both sides of the equation equal 16, your solution **x = 20** is verified. Verification ensures your solution holds true.

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

Would it be better to receive a \(5 \%\) raise and then, a year later, an \(8 \%\) raise or the other way around? Why?

Graph the solutions of \(|x|<3\) on the number line.

Match the sentence with one of the following: $$ a

Review operations with real numbers. Simplify. $$ -6.3+(-4.8) $$

The sum of two consecutive odd integers is less than \(100 .\) What is the largest pair of such integers?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Decision 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.