/*! 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 33 Solve each equation, and check y... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 33

Solve each equation, and check your solution. $$ 3 x+7=2 x+4 $$

Short Answer

Expert verified
The solution is \(x = -3\).

Step by step solution

01

Isolate Variable Terms

First, we need to get all the terms involving the variable on one side of the equation. Subtract \(2x\) from both sides of the equation: \[3x + 7 - 2x = 2x + 4 - 2x\] This simplifies to: \[x + 7 = 4 \]
02

Isolate the Variable

Next, isolate the variable \(x\) by getting rid of the constant term on the left side. Subtract 7 from both sides of the equation: \[x + 7 - 7 = 4 - 7\] This results in: \[x = -3\]
03

Check the Solution

Substitute \(x = -3\) back into the original equation to check if it satisfies the equation: \[3(-3) + 7 = 2(-3) + 4\] Simplify both sides: \[-9 + 7 = -6 + 4\] This results in: \[-2 = -2\] So, \(x = -3\) is indeed the correct solution.

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.

Isolating Variable Terms
One of the key steps in solving linear equations is isolating the variable terms. This means we want to get all the terms with the variable on one side of the equation. Let鈥檚 look at our exercise: Step 1: Subtract the smaller variable term from both sides: Given: 3x + 7 = 2x + 4 Subtract 2x from both sides: 3x + 7 - 2x = 2x + 4 - 2x This simplifies to: x + 7 = 4 We now have all the x terms on one side. This is isolating the variable terms.
Simplifying Equations
Simplifying equations involves performing operations to make the equation easier to solve. After isolating the variable term, our simplified equation is: x + 7 = 4 Next, we need to isolate x by removing the constant term (7). We do this by subtracting 7 from both sides: x + 7 - 7 = 4 - 7 This results in a simpler form: x = -3 We have now simplified the equation to find the value of x.
Checking Solutions
It's always essential to check the solution to ensure it satisfies the original equation. Substitute x = -3 back into the original equation: Original: 3x + 7 = 2x + 4 Substituting -3: 3(-3) + 7 = 2(-3) + 4 Simplify both sides: -9 + 7 = -6 + 4 This results in: -2 = -2 Since both sides are equal, our solution x = -3 is correct. Checking your work is crucial to verify that your answer is 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 problem. (Assume that all items are equally priced.) (In Exercises 53鈥�56, round answers to the nearest tenth.) See Example 6. If 9 pairs of jeans cost \(\$ 121.50,\) find the cost of 5 pairs.

A laptop computer with a regular price of \(\$ 597\) is on sale at \(20 \%\) off. Find the amount of the discount and the sale price of the computer.

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

Write the answer to each problem in terms of the variable. Claire has \(y\) dimes. Express the value of the dimes in cents.

Solve each formula for the specified variable. $$ y=m x+b \text { for } x $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.