Tìm x, biết:

a) To solve this equation, we can split it into two cases based on the sign of the expression inside the absolute value.

Case 1: 3x + 6 is positive
In this case, the equation becomes 3x + 6 - 12 = x + 1.
Simplifying, we get 2x - 6 = x + 1.
Subtracting x from both sides, we have x = 7.

Case 2: 3x + 6 is negative
In this case, the equation becomes -(3x + 6) - 12 = x + 1.
Simplifying, we get -3x - 6 - 12 = x + 1.
Combining like terms, we have -4x - 18 = x + 1.
Adding 4x to both sides, we get -18 = 5x + 1.
Subtracting 1 from both sides, we have -19 = 5x.
Dividing both sides by 5, we get x = -19/5.

Therefore, the solutions to the equation are x = 7 and x = -19/5.

b) To solve this equation, we can again split it into two cases based on the sign of the expressions inside the absolute values.

Case 1: x - 2 and 3x + 5 are both positive
In this case, the equation becomes x - 2 = 3x + 5.
Subtracting x from both sides, we get -2 = 2x + 5.
Subtracting 5 from both sides, we have -7 = 2x.
Dividing both sides by 2, we get x = -7/2.

Case 2: x - 2 and 3x + 5 are both negative
In this case, the equation becomes -(x - 2) = -(3x + 5).
Simplifying, we get -x + 2 = -3x - 5.
Adding x to both sides, we have 2 = -2x - 5.
Adding 5 to both sides, we get 7 = -2x.
Dividing both sides by -2, we have x = -7/2.

Therefore, the solution to the equation is x = -7/2.

c) To solve this equation, we need to isolate the absolute value expression.

12 - 4*|x + 1/2| = 0
Subtracting 12 from both sides, we get -4*|x + 1/2| = -12.
Dividing both sides by -4, we have |x + 1/2| = 3.

Now we can split this equation into two cases based on the sign of the expression inside the absolute value.

Case 1: x + 1/2 is positive
In this case, the equation becomes x + 1/2 = 3.
Subtracting 1/2 from both sides, we get x = 2.5.

Case 2: x + 1/2 is negative
In this case, the equation becomes -(x + 1/2) = 3.
Simplifying, we get -x - 1/2 = 3.
Adding 1/2 to both sides, we have -x = 3.5.
Multiplying both sides by -1, we get x = -3.5.

Therefore, the solutions to the equation are x = 2.5 and x = -3.5.

d) To solve this equation, we can again split it into two cases based on the sign of the expressions inside the absolute values.

Case 1: x - 3 and 2x - 6 are both positive
In this case, the equation becomes x - 3 + 2(2x - 6) = 0.
Simplifying, we get x - 3 + 4x - 12 = 0.
Combining like terms, we have 5x - 15 = 0.
Adding 15 to both sides, we get 5x = 15.
Dividing both sides by 5, we have x = 3.

Case 2: x - 3 and 2x - 6 are both negative
In this case, the equation becomes -(x - 3) + 2(2x - 6) = 0.
Simplifying, we get -x + 3 + 4x - 12 = 0.
Combining like terms, we have 3x - 9 = 0.
Adding 9 to both sides, we get 3x = 9.
Dividing both sides by 3, we have x = 3.

Therefore, the solution to the equation is x = 3.

e) To solve this equation, we can again split it into two cases based on the sign of the expression inside the absolute value.

Case 1: 4 - x is positive
In this case, the equation becomes 4 - x = 8 - 2x.
Adding x to both sides, we get 4 = 8 - x.
Subtracting 8 from both sides, we have -4 = -x.
Multiplying both sides by -1, we get 4 = x.

Case 2: 4 - x is negative
In this case, the equation becomes -(4 - x) = 8 - 2x.
Simplifying, we get -4 + x = 8 - 2x.
Adding 2x to both sides, we have -4 + 3x = 8.
Adding 4 to both sides, we get 3x = 12.
Dividing both sides by 3, we have x = 4.

Therefore, the solutions to the equation are x = 4 and x = 4.