Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 15

If \(|2 x-3|+2>7,\) which of the following could be the value of \(x ?\) Indicate all such values. a. -4 b. -3 c. -2 d. -1 e. 0 f. 1 g. 2 h. 3

Short Answer

Expert verified
The possible values of \(x\) that satisfy the inequality \(|2 x-3|+2>7\) are a. -4 b. -3, c. -2, and d. -1.

Step by step solution

01

Rewriting the Inequality

The initial absolute value inequality to solve is \(|2 x-3|+2>7\). To isolate the absolute value expression, rewrite the inequality as \(|2 x-3| > 7-2\) which simplifies to \(|2 x-3| > 5\).
02

Breaking Down the Absolute Value Inequality

The inequality \(|2 x-3| > 5\) can be broken down into two separate inequalities. These are \(2 x - 3 > 5\) and \(2 x - 3 < -5\).
03

Solving the First Inequality

Solving \(2 x - 3 > 5\) for \(x\) gives \(x > 4\).
04

Solving the Second Inequality

Solving \(2 x - 3 < -5\) for \(x\) gives \(x < -1\).
05

Testing the Provided Values

The possible values of \(x\) must satisfy one of the inequalities. By testing all the provided values, the set of values that fit the above inequalities are: a. -4 b. -3, c. -2 and d. -1.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

\(k>0\) \(l>1\) Quantity A \(\frac{1}{\frac{1}{k}+\frac{1}{l}}\) Quantity B \(\frac{k l}{\frac{1}{k}+\frac{1}{l}}\) a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

If \(4^{x}=1,024,\) then \(\left(4^{x+1}\right)\left(5^{x-1}\right)=\) a. \(10^{6}\) b. \(\left(5^{4}\right)\left(10^{5}\right)\) c. \(\left(4^{4}\right)\left(10^{5}\right)\) d. \(\left(5^{4}\right)\left(10^{4}\right)\) e. \(\left(4^{4}\right)\left(10^{4}\right)\)

Roberta drove 50 miles in 2 hours. Her rate in miles per hour is equivalent to which of the following proportions? Indicate all such proportions. a. 5 to 20 b. 100 to 4 c. 400 to 16 d. 20 to 500 e. 520 to 20

If 16 is the average (arithmetic mean) of \(p, 24,\) and \(q,\) what is \(16(p+q) ?\) a. 180 b. 192 c. 384 d. 524 e. 768

By which of the following could \(10\left(9^{6}\right)\) be divided by to produce an integer result? Indicate all such values. a. 90 b. 100 c. 330 d. 540 e. 720
See all solutions

Recommended explanations on English Textbooks

Single Paragraph Essay

Read Explanation

Essay Writing Skills

Read Explanation

Multiple Choice Questions

Read Explanation

Essay Plan

Read Explanation

Discourse

Read Explanation

Rhetorical Analysis 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.

Sign-up for free