Determine the real solutions of the inequalities- 1|x – 1|+ |r – 4| < 3;x2 – 5x + 4 < 0;1 –2х —(separately)!

Answered: Determine the real solutions of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Determine the real solutions of the inequalities
- 1
|x – 1|+ |r – 4| < 3;
x2 – 5x + 4 < 0;
1 –
2
х —
(separately)!

Expert Solution

Step 1

$F o r s o l v i n g t h e q u e s t i o n w e m u s t t h e f o l l o w i n g p r o p e r t i e s o f m o d u l u s i n e q u a l i t y - 1) I f a < b \Rightarrow - a > - b a n d i f a > b \Rightarrow - a < - b i . e . m u l t i p l i c a t i o n w i t h (- 1) w i l l c h a n g e t h e s i g n o f i n e q u a l i t y . 2) |x| = \{\begin{cases} x; i f x \geq 0 \\ - x; i f x < 0 . \end{cases} W e s o l v e t h e s e p r o b l e m s o n e b y o n e . S e e t h e f o l l o w i n g s t e p s -$

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