/*! 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 36 Solve the equation and check you... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 36

Solve the equation and check your solution. $$24-5 x=x$$

Short Answer

Expert verified
The solution to the equation is \(x = 4\)

Step by step solution

01

Simplify the Equation

Combine the terms that contain \(x\) to simplify the equation. This gives us \(24-5x = x\). By adding \(5x\) to both sides, we have \(24 = 6x\).
02

Solve for x

Now that we've isolated 6x on one side, we can solve for \(x\) by dividing both sides of the equation by 6 which gives \(x = 24/6 = 4\).
03

Check the Solution

Substitute \(x = 4\) back into the original equation to check the solution. The left-hand side of the equation is \(24-5*4 = 4\) and the right-hand side is \(x = 4\). Since the left side equals the right side, 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.

Equation Simplification
When solving a linear equation, the first goal is to simplify it to make it easier to work with. Consider the equation given:
  • \( 24 - 5x = x \)
We need to rearrange the terms containing the variable \(x\) as well as the constants. Start by adding \(5x\) to both sides of the equation. This helps in moving all \(x\) terms to one side, giving us:
  • \( 24 = 6x \)
To perform equation simplification effectively, follow these strategies:
  • Add or subtract terms to both sides to combine like terms.
  • Ensure your variables are on one side and constants on the opposite.
  • Continue simplifying until your equation takes its simplest form, with one variable term and one constant term.
This process of simplification lays the groundwork for the next steps in solving linear equations.
Variable Isolation
After simplifying the equation, our next focus turns to isolating the variable \(x\). From the simplified equation:
  • \( 24 = 6x \)
Here, \(x\) is multiplied by 6, so we need to isolate \(x\) by performing actions that "undo" this multiplication. Divide every term in the equation by 6:
  • \( x = \frac{24}{6} \)
This division gives us \(x = 4\). Isolating the variable makes the solution clear and straightforward. To consistently isolate variables:
  • Perform inverse operations (like division if it鈥檚 multiplication, or subtraction if it鈥檚 addition).
  • Whatever operation you perform on one side of the equation, do the same on the other side as well to maintain equality.
Isolating the variable helps in deriving a clear solution for \(x\) or any variable you are solving for.
Solution Verification
Verifying your solution confirms accuracy and avoids errors. With \(x = 4\), check it using the original equation:
  • Substitute \(x = 4\) back into \( 24 - 5x = x \).
  • Calculate the left side: \( 24 - 5 \times 4 = 24 - 20 = 4 \).
  • The right side is \(x = 4\).
Both sides equal 4, confirming the solution is correct. Follow these steps for verification:
  • Replace the variable with the derived value.
  • Simplify both sides of the equation independently.
  • Check that both sides of the equation are equal.
Solution verification is essential as it ensures the process you've done is correct and reliable.

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

Determine whether each value of \(x\) is a solution of the inequality. \(15-(x+8) \geq 13\) (a) \(x=0\) (b) \(x=-6\) (c) \(x=2\) (d) \(x=-10\)

Interest Rate Find the annual interest rate on a certificate of deposit that earned \(\$ 128.98\) interest in 1 year on a principal of \(\$ 1500\).

Match the statement with the property it represents. (a) Addition Property of Inequality (b) Subtraction Property of Inequality (c) Multiplication Property of Inequality (d) Division Property of Inequality \(3<9\), so \(3-1<9-1\).

Solve the proportion. $$\frac{3}{2}=\frac{9}{x}$$

Solve and graph the inequality. $$-10 x<40$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

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.