PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.3, Problem 66E
Solution

The equivalent inequality for the −3x<6 inequality from the given options.

The solution of the inequality is :

C. x>−2

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.3, Problem 66E , additional homework tip 1

Given:

The inequality, −3x<6 .

  1. 3x<6
  2. x<10
  3. x>−2
  4. x>2
  5. x>3

Concept Used:

  • If there is the strict inequality symbol < or> , then use a parenthesis on the interval
  • If there is the inequality symbol ≤ or≥ , then use a bracket on the interval
  • To graph the endpoint with strict inequality < or>, use the open parenthesis or a hollow circle at that endpoint.
  • To graph the endpoint with inequality symbol ≤ or≥, use the bracket or a solid circle at that endpoint.
  • Multiplying or dividing an inequality by a negative number reverse the inequality sign.

Calculation:

In order to solve the given inequality −3x<6 , first multiplying both sides by -1 it will reverse the inequality, then dividing both sides by 3 as shown below:

  −3x<6−3x−1>6−13x>−63x3>−63x>−2

Therefore, the solution of the inequality is option C.

The solution of the inequality is all real numbers that are greater than or equal to −2 . Since the inequality sign is not strict on the left endpoint, use a hollow circle at −2 .

The graph of the solution is shown below,

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.3, Problem 66E , additional homework tip 2

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Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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