/*! 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 Classify each of the following a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 6

Classify each of the following as either equivalent inequalities, equivalent equations, equivalent expressions, or not equivalent. $$ 2(4 x+1), 8 x+2 $$

Short Answer

Expert verified
Equivalent expressions.

Step by step solution

01

Expand the first expression

Expand the expression off: 2(4x + 1) Distribute the 2 to both terms inside the parentheses: 2 * 4x + 2 * 1 = 8x + 2.
02

Compare the expanded expression to the second expression

Compare the expanded expression 8x + 2 to the second given expression 8x + 2. Since they are exactly the same, the expressions are equivalent.
03

Classify the result

Based on the comparison, these are equivalent expressions.

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.

Expanding Expressions
Expanding expressions is an important skill in algebra. It involves removing parentheses to simplify an expression.
Let's take the example from the exercise: \[2(4x + 1)\]
We expand this expression by applying the distributive property. This means multiplying the 2 with each term inside the parentheses.
This gives us: \[2 \times 4x + 2 \times 1 = 8x + 2\]
After expanding, the original expression \[2(4x + 1)\] becomes the simpler form \[8x + 2\].
Understanding how to expand expressions makes it easier to see if two expressions are equivalent when simplified.
Distributive Property
The distributive property is a fundamental principle in algebra that makes it easier to handle expressions inside parentheses.
It states that a term outside the parentheses must be multiplied by each term inside the parentheses.
For example: \[a(b + c) = ab + ac\]
In the given exercise: \[2(4x + 1) \]
We use the distributive property to break it down:
  • Multiply 2 by 4x to get 8x
  • Multiply 2 by 1 to get 2
So, \[2(4x + 1) = 8x + 2\]
Using the distributive property simplifies the expression, helping us recognize equivalent expressions.
Comparison of Algebraic Expressions
Comparing algebraic expressions involves checking if the expanded forms are identical.
Let's revisit the exercise:
  • First given expression: \[2(4x + 1)\]
  • Second given expression: \[8x + 2\]
After expanding the first expression with the distributive property, we get: \[2(4x + 1) = 8x + 2\]
Both expressions simplify to \[8x + 2\], meaning they are equivalent.
This comparison shows that the original expressions are mathematically the same, despite looking different initially.
Understanding how to compare expressions helps solve many algebra problems, ensuring you arrive at the correct solution.

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

College Faculty. The number of part-time instructional faculty in U.S. postsecondary institutions is growing at a greater rate than the number of full-time faculty. The number of parttime faculty, in thousands, is approximated by $$ p(t)=27 t+325 $$ and the number of full-time faculty, in thousands, is approximated by $$ f(t)=16 t+500 $$ For both functions, \(t\) represents the number of years after \(1995 .\) Using an inequality, determine those years for which there were more part-time faculty than full-time faculty.

At one point during his presidency, a Gallup poll indicated that Barack Obama had an approval rating of \(42 \%,\) with a margin of error of \(3 \% .\) Write an inequality and interval notation for Obama's approval rating.

Solve. $$ \begin{aligned} 2 x-3 y &=5 \\ x+3 y &=-1 \end{aligned} $$

Explain in your own words why \(-7\) is not a solution of \(|x|<5\)

The reading difficulty of a textbook can be estimated by the Flesch Reading Ease Formula $$r=206.835-1.015 n-84.6 s$$ where \(r\) is the reading ease, \(n\) is the average number of words in a sentence, and s is the average number of syllables in a word. Sample reading- level scores are shown in the following table. $$\begin{array}{c|c} \hline \text { Score } & {\text { Reading Ease }} \\ \hline 90 \leq r \leq 100 & {5 \text { th grade }} \\ {60 \leq r \leq 70} & {8 \text { th and } 9 \text { th grades }} \\ {0 \leq r \leq 30} & {\text { College graduates }} \\ \hline\end{array}$$ The reading score for Alexa's new book for young adults indicates that it should be read with ease by \(8 t h-\) and 9 th-graders. If she averages 8 words per sentence, what is the average number of syllables per word?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

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.