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 for \(x\) are -4 and -3.

Step by step solution

01

Isolate the absolute value

Subtract 2 from both sides of the equation: \(|2x-3| > 7- 2\) which simplifies to \(|2x-3| > 5\)
02

Deal with the absolute value

Set up two equations, one for \(2x-3 > 5\) and one for \(2x-3 < -5\) based on the absolute value definition.
03

Solve the two equations

For \(2x-3 > 5\), add 3 to both sides and divide by 2, resulting in \(x > 4\). For \(2x - 3 < -5\), add 3 to both sides and divide by 2, resulting in \(x < -1\)
04

Check the solutions against the possible values

The equation is only true for \(x < -1\) or \(x > 4\). Compared to the given possibilities, the only solutions are therefore options a and b as only these fall into the result range we found.

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

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

If \(x, y,\) and \(z\) are consecutive odd integers where \(x

If three boys and three girls sit in a row on a park bench, and no boy can sit on either end of the bench, how many arrangements of the children on the bench are possible? a. 46,656 b. 38,880 c. 1,256 d. 144 e. 38

Joe has \(\$ 200 .\) If he buys a CD player for \(\$ 150,\) what is the greatest number of CDs he can buy with the remaining money if CDs cost \(\$ 12\) each?

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. \(\left(4^{4}\right)\left(10^{4}\right)\)
See all solutions

Recommended explanations on English Textbooks

Summary Text

Read Explanation

Prosody

Read Explanation

English Grammar

Read Explanation

Lexis and Semantics Summary

Read Explanation

Essay Plan

Read Explanation

Language and Social Groups

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