To solve the nonlinear inequality X+1s 0, we first observe that the numbers |(smaller value) and (larger value) are zeros of the numerator and denominator. These numbers divide the real line into three intervals. Complete the table. (-∞, (C Interval Sign of x + 1 Sign of x - 4 Sign of (x + 1)/(x - 4) Do any of the endpoints fail to satisfy the inequality? O Yes O No If so, which one(s)? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the solution of the inequality. (Enter your answer using interval notation.)

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.7: Graphing Linear Inequalities
Problem 14OE
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To solve the nonlinear inequality
x + :
< 0, we first observe that the numbers
(smaller value) and
(larger value) are zeros of the numerator and denominator. These numbers
divide the real line into three intervals. Complete the table.
(-a,
Interval
Sign of x + 1
? v
Sign of x - 4
Sign of (x + 1)/(x – 4)
Do any of the endpoints fail to satisfy the inequality?
O Yes
O No
If so, which one(s)? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
Find the solution of the inequality. (Enter your answer using interval notation.)
Transcribed Image Text:To solve the nonlinear inequality x + : < 0, we first observe that the numbers (smaller value) and (larger value) are zeros of the numerator and denominator. These numbers divide the real line into three intervals. Complete the table. (-a, Interval Sign of x + 1 ? v Sign of x - 4 Sign of (x + 1)/(x – 4) Do any of the endpoints fail to satisfy the inequality? O Yes O No If so, which one(s)? (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the solution of the inequality. (Enter your answer using interval notation.)
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