/*! 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 52 Solve each equation, and check y... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 52

Solve each equation, and check your solution. $$ 5 x+4-4 x=0 $$

Short Answer

Expert verified
The solution is x = -4, and it checks out.

Step by step solution

01

Combine Like Terms

First, combine the like terms on the left side of the equation. The equation is: \[ 5x + 4 - 4x = 0 \] Combine the terms involving x: \[ (5x - 4x) + 4 = 0 \] This simplifies to: \[ x + 4 = 0 \]
02

Isolate the Variable

Next, isolate x by subtracting 4 from both sides of the equation: \[ x + 4 - 4 = 0 - 4 \] This simplifies to: \[ x = -4 \]
03

Check the Solution

Substitute x = -4 back into the original equation to verify the solution: \[ 5(-4) + 4 - 4(-4) = 0 \] This simplifies to: \[ -20 + 4 + 16 = 0 \] Simplify further: \[ 0 = 0 \] Since both sides of the equation 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.

Combining Like Terms
Combining like terms is a crucial skill when solving linear equations. It involves simplifying an equation by adding or subtracting terms that have the same variable. For example, let鈥檚 look at the equation:
\(5x + 4 - 4x = 0\).
Here, both \(5x\) and \(-4x\) are like terms because they both contain the variable \(x\). Combining these like terms simplifies the equation:
\((5x - 4x) + 4 = 0\)
Which simplifies to:
\(x + 4 = 0\).
Once the like terms are combined, the equation becomes simpler and easier to solve. This step often reduces the number of terms and eases further steps.
Isolating the Variable
Isolating the variable means rearranging the equation to get the variable alone on one side. This helps us find its value. Using our simplified equation from the previous step:
\(x + 4 = 0\).
We can isolate \(x\) by subtracting 4 from both sides:
\(x + 4 - 4 = 0 - 4\).
This simplifies to:
\(x = -4\).
By performing the same operation on both sides of the equation, we maintain balance and correctly solve for \(x\). The goal is to have \(x\) isolated, making it straightforward to identify its value.
Checking the Solution
After isolating the variable and finding its value, it's important to ensure the solution is correct. To check, substitute the variable back into the original equation. For our solution \(x = -4\), substitute \(x\) into the original equation:
\(5(-4) + 4 - 4(-4) = 0\).
Simplify each term:
\(-20 + 4 + 16 = 0\).
This simplifies to:
\(0 = 0\).
Since both sides of the equation are equal, our solution \(x = -4\) is verified as correct. Checking solutions ensures the integrity of our calculations and confirms that our procedures are accurate.

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

Solve each equation. $$ -3 x=\frac{1}{4} $$

Write an equation using the information given in the problem. Use \(x\) as the variable. Then solve the equation. If twice a number is divided by \(5,\) the result is \(4 .\) Find the number.

Two cars leave towns 230 km apart at the same time, traveling directly toward one another. One car travels 15 km per hr slower than the other. They pass one another 2 hr later. What are their rates?

Solve each formula for the specified variable. \(P=4 s\) for \(s\)

For Exercises 69 and 70, (a) draw a sketch consisting of two right triangles depicting the situation described, and (b) solve the problem. (Source: Guinness World Records.) An enlarged version of the chair used by George Washington at the Constitutional Convention casts a shadow 18 ft long at the same time a vertical pole 12 ft high casts a shadow 4 ft long. How tall is the chair?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.