PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter P, Problem 62RE
Solution

The solution of the given inequality.

  52,6∪−1,52

Given information:

The inequality given is:

  2x−5<7 .

Formula used:

  • To solve an inequality, follow the steps below:

  1. Simplify the both sides of inequality.
  2. Take all the terms of variable on one side of the inequality and rest on other side of the inequality.
  3. Make the coefficient of variable 1.

  • For any x :

    •   x=x if x is positive−x if x is negative

  • Properties of inequality:

  1. b≤c⇒b±a≤c±a
  2. b≤c⇒ab≤ac, if a>0
  3. b≤c⇒ab≥ac, if a<0

Calculation:

In order to solve the given inequality:

  2x−5<7

First simplify the left side using for any x :

  x=x if x is positive−x if x is negative

Now, 2x−5 is positive if

  2x−5≥02x≥5x≥52

And negative for

  2x−5<02x<5x<52

Thus,

  for x≥522x−5=2x−5

Thus, the inequality can be rewritten as

  for x≥522x−5<7

Solve it by taking variable one side and rest other side and simplify, as

  for x≥522x−5<72x<7+52x<12x<122x<6

And case second

  for x<52The inequality is:−2x−5<7−2x+5<7−2x<7−5−2x<2

Now using the property of inequality b≤c⇒ab≥ac, if a<0 , by dividing both sides by −2 as:

  −2x−2>2−2x>−1

Thus, from case 1, the solution of given inequality is for x≥52 solution is x<6 , and for x≤52 solution is x>−1 this can be represented in interval form, as

  52,6∪−1,52

Thus, solution of given inequality is:

  52,6∪−1,52

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Chapter P, Problem 61RE
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Chapter P, Problem 63RE

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. P.1 - Prob. 1QRCh. P.1 - Prob. 2QRCh. P.1 - Prob. 3QRCh. P.1 - Prob. 4QRCh. P.1 - Prob. 5QRCh. P.1 - Prob. 6QRCh. P.1 - Prob. 7QRCh. P.1 - Prob. 8QRCh. P.1 - Prob. 9QRCh. P.1 - Prob. 10QR
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