/*! 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 6 Solve the equations. $$3 x=27$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 6

Solve the equations. $$3 x=27$$

Short Answer

Expert verified
The solution is \( x = 9 \).

Step by step solution

01

Identify the equation

The given equation is: \[ 3x = 27 \]
02

Isolate the variable

To solve for \( x \), isolate \( x \) by dividing both sides of the equation by 3. This gives: \[ x = \frac{27}{3} \]
03

Simplify the expression

Simplify the right side of the equation: \[ x = 9 \]

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 the Variable
One of the key strategies in solving linear equations is isolating the variable. This means getting the unknown variable (\(x\)in our case) by itself on one side of the equation.
To do this, we perform the same operation on both sides of the equation.In our given equation, \(3x = 27\),the variable \(x\)is being multiplied by 3.To isolate \(x\), we need to undo this multiplication by dividing both sides by 3.
After dividing, we get:\[ x = \frac{27}{3} \]By isolating the variable, we place ourselves a step closer to finding its value.
Simplify Expressions
Simplifying expressions is another important concept in basic algebra that often comes hand in hand with isolating the variable. Once you perform the necessary operations to isolate the variable, you may end up with an expression that still needs to be simplified.
In our equation, after isolating \(x\), we have:\[ x = \frac{27}{3} \]The expression \(\frac{27}{3}\)can be simplified. This means performing the division to find a simpler form:\[ x = 9 \]Simplifying expressions helps us get clear and straightforward answers, making calculations easier to understand and more accurate.
Basic Algebra
Understanding and applying basic algebra is essential for solving most equations. Basic algebra involves operations and manipulations of variables and constants to find unknown values.
For example, the given equation \(3x = 27\)is a simple algebraic equation that requires a basic understanding of multiplication and division to solve.
Here are some general steps in solving such equations:
  • Identify the equation and the variables involved.
  • Isolate the variable by performing operations like addition, subtraction, multiplication, or division on both sides.
  • Simplify the resulting expression to find the value of the variable.
Once these steps are mastered, solving more complex equations becomes manageable. Basic algebra forms the foundation for all higher-level math concepts, so it's crucial to have a good grasp of it from the start.

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

It is customary to leave a \(15-20 \%\) tip for the server in a restaurant. However, when you are at a restaurant in a social setting, you probably do not want to take out a pencil and piece of paper to figure out the tip. It is more socially acceptable to compute the tip mentally. Try this method. Step 1: First, if the bill is not a whole dollar amount, simplify the calculations by rounding the bill to the next-higher whole dollar. Step 2: Take \(10 \%\) of the bill. This is the same as taking one-tenth of the bill. Move the decimal point to the left 1 place. Step 3: If you want to leave a 20\% tip, double the value found in step 2. Step 4: If you want to leave a \(15 \%\) tip, first note that \(15 \%\) is \(5 \%+10 \% .\) Therefore, add one-half of the value found in step 2 to the number in step 2 . Estimate a \(20 \%\) tip on a bill of \(\$ 57.65\) (Hint: Round up to \$58 first.)

During a 5 -year period, the number of participants collecting food stamps went from 27 million to 17 million. What is the percent decrease? Round to the nearest whole percent.

To pass an exit exam, a student must pass a 60 -question test with a score of \(80 \%\) or better. What is the minimum number of questions she must answer correctly?

If a bank compounds interest quarterly for 2 years, how many total compounding periods are there?

Solve the equations. $$12 x=48$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.