/*! 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 3 Which of the following expressio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 3

Which of the following expressions is equivalent to \(7-2(y-1) ?\) (A) \(9-2 y\) (B) \(5-2 y\) (C) \(6-2 y\) (D) \(4+2 y\)

Short Answer

Expert verified
The expression equivalent to \(7 - 2(y-1)\) is Option (A) \(9 - 2y\).

Step by step solution

01

Identify the Expression to Simplify

The given expression is \( 7 - 2(y-1) \). We will simplify this expression to find which of the options it is equivalent to.
02

Distribute the Negative Sign

Apply the distributive property to \(-2(y-1)\) by multiplying \(-2\) with each term inside the parentheses: \(-2(y-1) = -2 \cdot y + (-2) \cdot (-1) = -2y + 2\).
03

Combine Terms

Now, substitute the simplified form of \(-2(y-1)\) back into the original expression: \(7 - 2(y-1) = 7 + (-2y + 2) = 7 + 2 - 2y\).
04

Complete the Simplification

Combine the constants: \(7 + 2 = 9\). Thus, the simplified expression is \(9 - 2y\).
05

Find the Equivalent Expression

The simplified expression after all steps is \(9 - 2y\). Now, compare this with the provided options to find the equivalent expression: Option (A) \(9 - 2y\), Option (B) \(5 - 2y\), Option (C) \(6 - 2y\), Option (D) \(4 + 2y\). The expression \(9 - 2y\) is equivalent to Option (A).

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.

Distributive Property
To successfully solve math equations, understanding the distributive property is key. It allows you to remove parentheses in an expression by distributing or multiplying the outside term with each term inside the parentheses.

In this exercise, you apply it to the expression \(-2(y-1)\) by multiplying \(-2\) with all terms inside the bracket. Here's how it goes:
  • Multiply \(-2\) with \(y\) and get \(-2y\).
  • Then, multiply \(-2\) with \(-1\) and remember that multiplying two negatives gives a positive, resulting in \(+2\).
The expression simplifies to \(-2y + 2\). This step reduces the complexity of the equation by managing parentheses, turning it into a more straightforward form. It's like peeling off layers to see the core of the problem beautifully simplified.
Combining Like Terms
Now that you have an expression without parentheses, it's time to combine like terms. This step is about simplifying the expression by grouping similar terms together.

In \(7 + 2 - 2y\), you identify that \(7\) and \(2\) are constants. Combining them together:
  • Add \(7\) and \(2\) to get \(9\)
You are left with \(9-2y\).

Remember, like terms share the same variable raised to the same power. It's like seeing apples and oranges. By adding all the apples together, you can simplify and more easily work with your group of fruit. So, combining terms makes solving the equation easier and quicker.
Equivalent Expressions
After simplification using distributive property and combining terms, you end up with an expression that is easier to handle, \(9 - 2y\). But the big question is, how do you know it鈥檚 equivalent to one of the given options?

An equivalent expression means despite looking different initially, they hold the same value when calculated. Comparing the simplified expression \(9 - 2y\) with the options:
  • Option (A) is \(9 - 2y\), which matches exactly.
  • Other options either mismatch numerically or have different operations.
So, the expression \(7 - 2(y-1)\) is equivalent to \(9 - 2y\) as seen in Option (A). Having confidence in identifying equivalent expressions ensures you can simplify complex equations into manageable, recognizably equal terms!

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

What is the value of \(x\) in the following equation? \(3 x+2=\frac{4}{3} x\) (A) \(-\frac{6}{5}\) (B) \(-\frac{6}{5}\) (C) \(\frac{4}{6}\) (D) \(\frac{7}{9}\)

An animal shelter can house only cats and dogs. Each dog requires 2 cups of food and 3 treats a day, while each cat requires 1 cup of food a day and 2 treats a day. If the shelter has available a total of 400 cups of food and 500 treats a day, what expressions portray the full scope of the number of \(c\) cats and dogs the shelter could potentially house? (A) \(2 \mathrm{~d}-\mathrm{c} \leq 400\) and \(3 \mathrm{~d}+\mathrm{c}<500\) (B) \(2 d+c \leq 400\) and \(3 d+2 c \leq 500\) (C) \(4 \mathrm{~d}+\mathrm{c}<400\) and \(\mathrm{d}+\mathrm{c}<500\) (D) \(2 \mathrm{~d}+2 \mathrm{c} \leq 400\) and \(2 \mathrm{~d}+3 \mathrm{c} \leq 500\)

First solve the problem, and then enter your answer on the grid provided on the answer sheet. The instructions for entering your answers follow. On a particular college campus, there are two men for every three women. If the total number of men and women on campus is equal to 4,000 , how many more women are there on campus than men?

A line has the equation \(y-4 x=5\). What is the slope of a line that is perpendicular to this line? (A) \(-4\) (B) \(-\frac{1}{4}\) (C) \(\frac{4}{3}\) (D) 4

Which of the following would provide the most specific and relevant elaboration to conclude this sentence? (A) NO CHANGE (B) are \(2.5\) times as likely as those with a basic reading ability to earn \(\$ 850\) or more per week. (C) are twice as likely as those who do not read to spend over \(\$ 100\) a year on books and periodicals. (D) are demonstrably more effective at remembering not just the broad ideas of what they read, but the finer details.
See all solutions

Recommended explanations on English Textbooks

Essay Writing Skills

Read Explanation

Key Concepts in Language and Linguistics

Read Explanation

Language Acquisition

Read Explanation

English Language Study

Read Explanation

Multiple Choice Questions

Read Explanation

5 Paragraph Essay

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.