Solve the inequality. |3x + 6| < 12 a) –6 < x < 2 b) –21 < x < 3 c) –6 > x > 2 d) –2 < x < 2

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Step-by-step explanation:

|3x+6|<12

One solution was found :

                     -6 < x < 2

Absolute Value Inequality entered :

     |3x+6|<12

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

     |3x+6| < 12

Step  2  :

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |3x+6|

For the Negative case we'll use -(3x+6)

For the Positive case we'll use (3x+6)

Step  3  :

Solve the Negative Case

     -(3x+6) < 12

    Multiply

     -3x-6 < 12

    Rearrange and Add up

     -3x < 18

    Divide both sides by 3

     -x < 6

    Multiply both sides by (-1)

    Remember to flip the inequality sign

     x > -6

    Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

     (3x+6) < 12

    Rearrange and Add up

     3x < 6

    Divide both sides by 3

     x < 2

    Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

   -6 < x < 2

Solution in Interval Notation

   (-6,2)

Solution on the Number Line

One solution was found :

                     -6 < x < 2

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

answer: b)

step-by-step explanation:

its a dot plot because since the score is not high numbers.

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