PRECALCULUS:...COMMON CORE ED.-W/ACCESS
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
10th Edition
ISBN: 9780134781839
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
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Chapter P.7, Problem 48E
Solution

The solution set of the absolute value inequality 2x2+3x20>10 .

  ,4.693.11,1.613.19,

Given:

The absolute value inequality 2x2+3x20>10 .

Concept used:

  • Absolute value inequality states that, if x<a , then the solutions are a<x<a .
  • The value of an absolute value function is always greater than or equal to 0.
  • If there is the strict inequality symbol < or> , then use a parenthesis on the interval
  • If there is the inequality symbol  or , then use a bracket on the interval
  • To graph the endpoint with strict inequality < or>, use the open parenthesis or a hollow circle at that endpoint.
  • To graph the endpoint with inequality symbol  or, use the bracket or a solid circle at that endpoint.
  • Multiplying or dividing an inequality by a negative number reverse the inequality sign.

Calculation:

In order to solve the given absolute value inequality, use the definition of absolute value function and simplify further as shown below

  2x2+3x20>102x2+3x2010>10102x2+3x2010>0

In order to solve the inequality, plot the graph of the function 2x2+3x2010 and locate the intervals where the graph is above the x -axis.

The graph of the function is shown below,

  PRECALCULUS:...COMMON CORE ED.-W/ACCESS, Chapter P.7, Problem 48E

Thus, the solution set of the given absolute value inequality is ,4.693.11,1.613.19, .

Chapter P Solutions

PRECALCULUS:...COMMON CORE ED.-W/ACCESS

Ch. P.1 - Prob. 1ECh. P.1 - Prob. 2ECh. P.1 - Prob. 3ECh. P.1 - Prob. 4ECh. P.1 - Prob. 5ECh. P.1 - Prob. 6ECh. P.1 - Prob. 7ECh. P.1 - Prob. 8ECh. P.1 - Prob. 9ECh. P.1 - Prob. 10ECh. P.1 - Prob. 11ECh. P.1 - Prob. 12ECh. P.1 - Prob. 13ECh. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - Prob. 17ECh. P.1 - Prob. 18ECh. P.1 - Prob. 19ECh. P.1 - Prob. 20ECh. P.1 - Prob. 21ECh. P.1 - Prob. 22ECh. P.1 - Prob. 23ECh. P.1 - Prob. 24ECh. P.1 - Prob. 25ECh. P.1 - Prob. 26ECh. P.1 - Prob. 27ECh. P.1 - Prob. 28ECh. P.1 - Prob. 29ECh. P.1 - Prob. 30ECh. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Prob. 33ECh. P.1 - Prob. 34ECh. P.1 - Prob. 35ECh. P.1 - Prob. 36ECh. P.1 - Prob. 37ECh. P.1 - Prob. 38ECh. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Prob. 42ECh. P.1 - Prob. 43ECh. P.1 - Prob. 44ECh. P.1 - Prob. 45ECh. P.1 - Prob. 46ECh. P.1 - Prob. 47ECh. P.1 - In Exercises 4752, simplify the expression. Assume...Ch. 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