Problem 22 Solve. Be sure to check. $$ ... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 22

Solve. Be sure to check. $$ 6 \cdot x=42 $$

Short Answer

Expert verified

The solution is $x = 7$.

Step by step solution

Understand the Equation

The given equation is a simple linear equation in the form of $6 \times x = 42$. The goal is to find the value of $x$ that makes this equation true.

Isolate the Variable

To isolate $x$, divide both sides of the equation by 6. This gives: $ \frac{6 \times x}{6} = \frac{42}{6} $

Simplify the Equation

Simplify both sides of the equation: $ x = 7 $. This is the value of $x$ that satisfies the equation.

Check the Solution

Verify the solution by substituting $x = 7$ back into the original equation: $6 \times 7 = 42$ Since both sides are equal, 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.

Isolating Variables

When solving linear equations, one of the primary steps involves isolating the variable. This means you need to get the variable you're solving for by itself on one side of the equation. In our example, we start with the equation:

\[ 6 \times x = 42 \]

To isolate the variable $ x $, you need to perform the inverse operation of what's being done to $ x $. Here, $ x $ is being multiplied by 6. The inverse of multiplication is division. Therefore, divide both sides of the equation by 6:

\[ \frac{6 \times x}{6} = \frac{42}{6} \]

This simplifies the equation and isolates the variable $ x $ on one side.

Simplifying Equations

Once you've isolated the variable, the next step is to simplify the equation. Simplification involves performing any arithmetic calculations that allow you to solve for the variable. Using the previous step:

\[ \frac{6 \times x}{6} = \frac{42}{6} \]

Simplify the left side:

\[ x \]

Simplify the right side:

\[ 7 \]

Therefore, the simplified equation becomes $ x = 7 $.

Remember, simplification is crucial for making the equation easier to understand and solving it efficiently.

Checking Solutions

The final step is to check your solution. This ensures that the value you found is indeed correct. To check the solution, substitute the value of the variable back into the original equation and verify that both sides are equal. For the given example, substitute $ x = 7 $ into the original equation $ 6 \times x = 42 $:

\[ 6 \times 7 = 42 \]

Since both sides of the equation are equal, $ 42 = 42 $, the solution $ x = 7 $ is correct.

Checking solutions helps confirm the accuracy of your work and ensures no mistakes were made during the solving process.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve. Be sure to check. $$ 6 \cdot x=42 $$

Short Answer

Step by step solution

Understand the Equation

Isolate the Variable

Simplify the Equation

Check the Solution

Key Concepts

Isolating Variables

Simplifying Equations

Checking Solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.