/*! 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 51 \(1.4 x-3=0.4 x\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 51

\(1.4 x-3=0.4 x\)

Short Answer

Expert verified
x = 3

Step by step solution

01

- Move all terms involving x to one side

To solve the equation for x, start by moving all terms involving x to one side of the equation. Subtract \(0.4x\) from both sides:\[1.4x - 0.4x - 3 = 0\]
02

- Simplify the equation

Combine the terms involving x on the left side:\[ (1.4 - 0.4)x - 3 = 0 \]This simplifies to:\[ 1.0x - 3 = 0 \]
03

- Solve for x

Isolate x by adding 3 to both sides of the equation:\[ 1.0x = 3 \]Then divide by 1.0:\[ x = 3 \]

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.

Moving Terms
In solving linear equations, the first step often involves moving terms to one side. Here, we need to gather all the variables involving x together.
For the equation \(1.4x - 3 = 0.4x\), we can start by moving the term \(0.4x\) to the opposite side.
This is done by performing the same operation on both sides of the equation. We subtract \(0.4x\) from both sides:
\[1.4x - 3 - 0.4x = 0.4x - 0.4x\]
This simplifies to:
\[1.4x - 0.4x - 3 = 0\]
Breaking it down helps to maintain the balance of the equation. Ensuring that all terms are correctly moved is crucial for accurate solution.
Isolating Variables
Once the terms are correctly placed, the next step is isolating the variable. To isolate x in the equation \(1.0x - 3 = 0\), we need to get x alone on one side of the equation.
This involves removing the constant term next to x. In our example, we isolate x by adding 3 to both sides:
\[1.0x - 3 + 3 = 0 + 3\]
By adding or subtracting the same number on both sides of the equation, we maintain equality. The equation simplifies to:
\[1.0x = 3\]
This step is all about making sure that x is by itself, with no other numbers or variables attached to it.
Simplifying Equations
Finally, it's important to simplify the equation to find the value of the variable. In our example, \(1.0x = 3\), x needs to be alone.
We do this by dividing both sides by \(1.0\):
\[x = 3\]
Simplification means reducing the equation to its simplest form. Every arithmetic step should bring you closer to the simplest form of the equation so that the solution is clear.
Always double-check by substituting back into the original equation to ensure correctness.

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

The Toyota Camry and the Honda Civic were the top-selling passenger cars in the United States in \(2016 .\) Civic sales were 22 thousand less than Camry sales, and 756 thousand of the two cars were sold. How many of each car were sold? (Data from wwy, businessinsider,com

Find the measure of an angle whose complement is four times its measure. (Hint: If \(x\) represents the measure of the unknown angle, how would we represent its complement?)

An office manager booked 55 airline tickets. He booked 7 more tickets on American Airlines than United Airlines. On Southwest Airlines, he booked 4 more than twice as many tickets as on United. How many tickets did he book on each airline?

Solve each formula for the specified variable. \(A=p(1+r t)\) for \(t\)

Solve each equation for \(y\) $$ -2 x+3 y=-9 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

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.