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

step-by-step explanation:

given perimeter: 28cm

length: 9cm

atp,

2(l+w)=p of the reactangle

2(9+x)=28

18+2x=28

2x=28-18

x=10/2

x=5

therefore width is 5 cm