/*! 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 2 Solve each linear equation. $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 2

Solve each linear equation. $$6 x-3=63$$

Short Answer

Expert verified
The solution to the equation \(6x - 3 = 63\) is \(x = 11\).

Step by step solution

01

Simplify the Equation

Start by simplifying the equation, keeping the variable on one side and the remaining terms on the other side. The equation becomes \(6x = 63 + 3\).
02

Further Simplify

Now, further simplify either side of the equation. Therefore, the equation simplifies to \(6x = 66\).
03

Solve for the Variable

To solve for x, divide 66 by 6. So, \(x = 66 / 6 = 11\).

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.

Solving Equations
Solving equations is like being a detective, where your goal is to find the value of the unknown variable. To uncover the mystery, you need to rearrange the equation so that the variable ends up alone on one side. For our exercise, we dealt with the linear equation:
  • Start by analyzing both sides of the equation.
  • Perform operations to isolate the variable.
In our example, we started with the equation: \(6x - 3 = 63\). The first step was to eliminate `-3` by adding `3` to both sides. This centers the focus on the term containing the variable. Always remember, anything you do to one side of the equation, you must do to the other. This keeps the equation balanced, just like a perfectly balanced scale.
Simplification
Simplification is like tidying up your room. You need to get everything in order so you can clearly see what you are working with. Think of it as making the equation "clean" and simple to solve. In the original exercise:
  • The first simplification involved rearranging the equation \(6x - 3 = 63\) to \(6x = 66\).
  • This was done by adding 3 to both sides, getting rid of the extra number on the left side.
Now, the equation was reduced to just terms involving the variable on one side. With this, our equation was much easier to handle. Simplification also helps to ensure that no unnecessary figures distract from solving for the variable.
Variables
Variables are like the hidden treasure you need to find in equations. They're usually represented by letters like \(x\) or \(y\). In our case, the variable is \(x\). So, what are variables exactly? Here鈥檚 a quick guide:
  • They are placeholders for unknown values. Imagine them as puzzle pieces waiting for their correct number.
  • Variables can change depending on the context of the problem, but they usually represent something we want to figure out.
In solving our equation, the end goal was to determine what value of \(x\) makes the equation true. We found \(x = 11\) by performing operations that gradually unveiled the value of our mysterious variable. Thus, this insight fulfills our quest to unlock the essence of the equation.

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

Exercises \(159-161\) will help you prepare for the material covered in the next section. In parts (a) and (b), complete each statement. a. \(\frac{b^{7}}{b^{3}}=\frac{b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b}{b \cdot b \cdot b}=b^{2}\) b. \(\frac{b^{8}}{b^{2}}=\frac{b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b \cdot b}{b \cdot b}=b^{?}\) c. Generalizing from parts (a) and (b), what should be done with the exponents when dividing exponential expressions with the same base?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$8^{-\frac{1}{3}}=-2$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \((2 x-3)^{2}=25\) is equivalent to \(2 x-3=5\)

What does it mean to factor completely?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. Parts for an automobile repair cost \(\$ 175 .\) The mechanic charges \(\$ 34\) per hour. If you receive an estimate for at least \(\$ 226\) and at most \(\$ 294\) for fixing the car, what is the time interval that the mechanic will be working on the job?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.