x^2+3x+10<3x^2-15x+26 solve ineq

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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x^2+3x+10<3x^2-15x+26 solve ineq

Expert Solution
Step 1: We have given an inequality to solve

x squared plus 3 x plus 10 less than3 x squared minus 15 x plus 26

0 less than 3 x squared minus x squarednegative 15 x minus 3 x plus 26negative 10

0 less than 2 x squared minus 18 xplus 16

0 less than 2 left parenthesis x squared minus 9 xplus 8 right parenthesis

0 less than 2 left parenthesis x squared minus x minus 8 xplus 8 right parenthesis

0 less than 2 left parenthesis x open parentheses x minus 1 close parenthesesnegative 8 open parentheses x minus 1 right parenthesis close parentheses

0 less than 2 open parentheses x minus 1 close parenthesesopen parentheses x minus 8 close parentheses

0 less than f open parentheses x close parentheses

Let,

f open parentheses x close parentheses equals 2 open parentheses x minus 1 close parenthesesopen parentheses x minus 8 close parentheses

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