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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