/*! 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 13 Solve each equation, and check t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 13

Solve each equation, and check the solution. \(2 x+5=4 x-3\)

Short Answer

Expert verified
x = 4

Step by step solution

01

Isolate variable terms on one side

Move all variable terms to one side of the equation. Subtract 2x from both sides of the equation: \[2x + 5 - 2x = 4x - 3 - 2x\]. This simplifies to: \[5 = 2x - 3\].
02

Isolate the variable

Next, move all constants to the other side by adding 3 to both sides:\[5 + 3 = 2x - 3 + 3\]. This simplifies to: \[8 = 2x\].
03

Solve for x

Now solve for x by dividing both sides of the equation by 2:\[x = \frac{8}{2}\]. This gives: \[x = 4\].
04

Check the solution

Substitute x = 4 back into the original equation to ensure it holds true: \[2(4) + 5 = 4(4) - 3\]. This simplifies to: \[8 + 5 = 16 - 3\]. Which gives: \[13 = 13\]. 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.

isolate variable
One of the first steps in solving a linear equation is to isolate the variable. This means getting the variable alone on one side of the equation. It's like cleaning up a messy room 鈥� we want to separate the 'variable clutter' from everything else.
For example, in the equation \(2x + 5 = 4x - 3\), we start by moving the variable terms to one side. We do this by subtracting \(2x\) from both sides of the equation:
\[2x + 5 - 2x = 4x - 3 - 2x\]
After cancelling out the \(2x\) on the left side, we get:
\[5 = 2x - 3\]
Now, our variable \(x\) is only on the right side, and we're one step closer to solving it!
step by step solution
Solving an equation involves breaking down the problem into manageable steps. Each step simplifies the equation, and brings us closer to finding the value of the variable.
After isolating the variable term, we take the following steps:
  • Move constants to the other side by adding or subtracting.
  • Divide or multiply to solve for the variable.

Continuing our example, once we have \(5 = 2x - 3\), we need to move the constant -3 to the other side.
We do this by adding 3 to both sides:
\[5 + 3 = 2x - 3 + 3\]
This simplifies to:
\[8 = 2x\]
Finally, solve for \(x\) by dividing both sides by 2:
\[x = \frac{8}{2}\]
This gives us:
\[x = 4\]
Following each step methodically ensures we don't miss any important details.
check the solution
Once you have found the solution, it's crucial to verify it. Checking the solution ensures that our answer satisfies the original equation.
Substitute the solution back into the original equation to see if both sides are equal. In our example, substitute \(x = 4\) back into \(2x + 5 = 4x - 3\):
\[2(4) + 5 = 4(4) - 3\]
This simplifies to:
\[8 + 5 = 16 - 3\]
Which gives:
\[13 = 13\]
Since both sides of the equation are equal, our solution \(x = 4\) is correct.
Always remember to check your solutions. It's a quick and easy way to make sure your work is accurate. Trustworthy results come from this verification step.

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 value of a "Mint State-63" (uncirculated) 1950 Jefferson nickel minted at Denver is twice the value of a 1945 nickel in similar condition minted at Phil- adelphia. Together, the total value of the two coins is \(\$ 24.00 .\) What is the value of each coin? (Data from Yeoman, R., A Guide Book of United States Coins.)

The sum of a number and 9 is \(-26 .\) What is the number?

Solve each formula for the specified variable. \(\mathscr{A}=\frac{1}{2} h(b+B)\) for \(b\)

The world's largest taco contained approximately \(1 \mathrm{~kg}\) of onion for every \(6.6 \mathrm{~kg}\) of grilled steak. The total weight of these two ingredients was \(617.6 \mathrm{~kg}\). To the nearest tenth of a kilogram, how many kilograms of each ingredient were used to make the taco? (Data from Guinness World Records.

During the 115 th session, the U.S. Senate had a total of 98 Democrats and Republians. There were 6 fewer Democrats than Republicans. How many members of each party were there? (Data from www. senate.gov)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.