PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
10th Edition
ISBN: 9780136174318
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter P, Problem 69RE
Solution

The solution of the given inequality.

  −∞,−19∪9,∞

Given information:

The inequality given is:

  x+57>2 .

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 equals 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:

      x+57>2

    First simplify the left side using for any x :

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

    Now, x+57 is positive if

      x+57≥0x+5≥0x≥−5

    And negative for

      x≤−5

    Thus,

      x+57=x+57 if x≥−5−x−57 if x≤−5

    Thus, the inequality can be rewritten as

      for x≥−5x+57>2

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

      x+57>2x+5>2×7x>14−5x>9

    And case second

      for x≤−5The inequality is:−x−57>2−x−5>2×7−x>14+5−x>19x<−19

    Thus, from case 1, the solution of given inequality is for x≥−5 solution is x>9 .And for x≤−5 solution is x<−19 this can be represented in interval form, as

      −∞,−19∪9,∞

    Thus, solution of given inequality is:

      −∞,−19∪9,∞

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Chapter P, Problem 68RE
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Chapter P, Problem 70RE

Chapter P Solutions

PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)

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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