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 61RE
Solution

The solution of the given inequality.

  x≤13 , −∞,13

Given information:

The inequality given is:

  3x−54≤−1 .

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.

  • 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:

  3x−54≤−1

First simplify it using the property of inequality b≤c⇒ab≤ac, if a>0 , by multiplying 4 to both sides as:

  3x−54×4≤−1×43x−5≤−4

Now, take the variables on one side of inequality and rest on other side, as:

  3x−5+5≤−4+53x−0≤13x≤1

Now in order to make the coefficient of variable x 1, divide both side with 3, as

  3x3≤13x≤13

Thus, the solution of given inequality is every number less than or equals to 13 , this can be represented in interval form, as

  −∞,13

Thus, solution of given inequality is:

  x≤13 , or interval form −∞,13

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Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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