/*! 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 68 Solve. $$ 2.1(3-x)=8.4 $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 68

Solve. $$ 2.1(3-x)=8.4 $$

Short Answer

Expert verified
x = -1

Step by step solution

01

Distribute the 2.1

First, distribute the 2.1 to both terms inside the parentheses. The equation becomes:\[2.1 \times 3 - 2.1 \times x = 8.4\]This simplifies to:\[6.3 - 2.1x = 8.4\]
02

Isolate the variable term

Next, move the constant term to the other side of the equation by subtracting 6.3 from both sides:\[6.3 - 2.1x - 6.3 = 8.4 - 6.3\]This simplifies to:\[-2.1x = 2.1\]
03

Solve for x

Finally, isolate x by dividing both sides of the equation by -2.1:\[x = \frac{2.1}{-2.1}\]This simplifies to:\[x = -1\]

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.

distributive property
The distributive property is a simple yet powerful concept in algebra. It allows you to multiply a single term by all terms inside parentheses. For example, in the equation \[2.1(3-x)=8.4\], you need to distribute the 2.1 to both the 3 and the \(-x\). This is done by multiplying 2.1 by each term within the parentheses. The equation then turns into \[2.1 \times 3 - 2.1 \times x = 8.4 \]. Distributing helps to simplify complex equations, making them easier to solve.
isolating variables
Isolating the variable is crucial in solving linear equations. It means getting the variable alone on one side of the equation. To isolate the variable in the equation \[6.3 - 2.1x = 8.4\], you need to move the constant term to the other side. This is done by performing arithmetic operations on both sides of the equation. Subtract 6.3 from both sides to get \[-2.1x = 2.1\]. Isolating the variable helps to clearly visualize what needs to be done next.
solving for x
Finally, solving for x means finding the value of x that makes the equation true. Once the variable is isolated, as in \(-2.1x = 2.1\), you can solve for x by performing the inverse operation. Here, divide both sides by -2.1 to get \[x = \frac{2.1}{-2.1}\]. This simplifies to \[x = -1\]. Solving for the variable lets you find the specific value it holds in the equation.

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 to an algebraic expression. The product of the difference of two numbers and their sum

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 43-(-9+2)^{2}+18 \div 6 \cdot(-2) $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ (-4)^{2} $$

Write an equivalent expression using an associative law. $$ -7(a b) $$

Find an equivalent expression by factoring. $$ a b+b $$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

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.