/*! 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 199 Solve the following equations wi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 199

Solve the following equations with variables and constants on both sides. $$6 x-17=5 x+2$$

Short Answer

Expert verified
x = 19

Step by step solution

01

Move variables to one side

Subtract 5x from both sides of the equation to get rid of the variable on the right side. This leaves:\[ 6x - 5x - 17 = 2 \]Simplify it to:\[ x - 17 = 2 \]
02

Isolate the variable

Add 17 to both sides of the equation to isolate the variable x on the left side. This results in:\[ x - 17 + 17 = 2 + 17 \]Which simplifies to:\[ x = 19 \]

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.

Equations with Variables on Both Sides
When solving equations with variables on both sides, the goal is to get all the variables on one side of the equation. This simplifies the equation and makes it easier to solve.

In the given exercise, the equation is: $$6x - 17 = 5x + 2$$.

Here, you have variables (x) on both sides of the equal sign. The first step involves moving the variables to one side. This helps in isolating the variable and proceeding with simpler arithmetic operations later.
Isolating the Variable
Isolating the variable means getting the variable alone on one side of the equation. This is crucial because it allows us to solve for the variable directly.

From the above step, we know that we need to subtract \(5x\) from both sides to move all x terms to one side. This results in: [ 6x - 5x - 17 = 2 Simplifying, we get: ] [ x - 17 = 2 Now, add 17 to both sides of the equation to isolate x: ] [ x - 17 + 17 = 2 + 17 Simplifying further, we obtain: ] [ x = 19 . Through these steps, we've successfully isolated x and found its value.
Simplify Mathematical Expressions
Simplifying mathematical expressions makes the equation more manageable. In the earlier steps, we simplified by combining like terms and performing basic arithmetic operations.

In our example, combining like terms is shown when we simplified [ 6x - 5x into [ x . This straightforward simplification allows us to isolate the variable more easily.

Always remember to:
  • Combine like terms.
  • Perform arithmetic operations carefully.
  • Keep the equation balanced by doing the same operation on both sides.


Following these simplification techniques ensures accuracy and ease when solving linear equations.

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 inequality, graph the solution on the number line, and write the solution in interval notation. $$20>\frac{2}{5} h$$

Fighter pilots The maximum height, \(h\), of a fighter pilot is 77 inches. Write this as an inequality.

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$\frac{m}{18} \geq-4$$

Translate and solve. Then write the solution in interval notation and graph on the number line. Three more than \(h\) is no less than \(25 .\)

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$9 u+5(2 u-5) \geq 12(u-1)+7 u$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Calculus

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.