Respuesta :
Answer:
x=-3
Step-by-step explanation:
Step 1 :
Rearrange this Absolute Value Equation
Absolute value equalitiy entered
|2x+6| = 2x+6
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 |2x+6|
For the Negative case we'll use -(2x+6)
For the Positive case we'll use (2x+6)
Step 3 :
Solve the Negative Case
-(2x+6) = 2x+6
Multiply
-2x-6 = 2x+6
Rearrange and Add up
-4x = 12
Divide both sides by 4
-x = 3
Multiply both sides by (-1)
x = -3
Which is the solution for the Negative Case
Step 4 :
Solve the Positive Case
(2x+6) = 2x+6
Rearrange and Add up
0x = 0
False, No solution for the Positive Case
Step 5 :
Wrap up the solution
When an absolute value equation has just one solution, that solution has to be checked:
Check the negative case solution
The equality is |2x+6| = 2x+6
The solution is x = -3
We check the solution by plugging it for x
|2(-3)+6| = 2(-3)+6
The left hand side is equal to (0)
The right hand side is equal to (0)
The two sides are equal!
Solution checks!
x=-3
Hope this helps
