Tìm x, biết: 2|2x - 3| - 1 = 5

a) 2|2x-3| - 1 = 5
To solve this equation, we need to isolate the absolute value term.
First, we add 1 to both sides of the equation:
2|2x-3| = 6
Next, we divide both sides by 2:
|2x-3| = 3
Now, we have two cases to consider:
1) 2x-3 = 3
Solving for x, we add 3 to both sides:
2x = 6
Dividing both sides by 2:
x = 3
2) -(2x-3) = 3
Expanding the negative sign:
-2x + 3 = 3
Subtracting 3 from both sides:
-2x = 0
Dividing both sides by -2:
x = 0
Therefore, the solutions to the equation are x = 3 and x = 0.

b) 15 - 2|3x+1| = 7
To solve this equation, we need to isolate the absolute value term.
First, we subtract 7 from both sides of the equation:
-2|3x+1| = -8
Next, we divide both sides by -2:
|3x+1| = 4
Now, we have two cases to consider:
1) 3x+1 = 4
Solving for x, we subtract 1 from both sides:
3x = 3
Dividing both sides by 3:
x = 1
2) -(3x+1) = 4
Expanding the negative sign:
-3x - 1 = 4
Adding 1 to both sides:
-3x = 5
Dividing both sides by -3:
x = -5/3
Therefore, the solutions to the equation are x = 1 and x = -5/3.

c) 4|3x-2| + 5 = 17
To solve this equation, we need to isolate the absolute value term.
First, we subtract 5 from both sides of the equation:
4|3x-2| = 12
Next, we divide both sides by 4:
|3x-2| = 3
Now, we have two cases to consider:
1) 3x-2 = 3
Solving for x, we add 2 to both sides:
3x = 5
Dividing both sides by 3:
x = 5/3
2) -(3x-2) = 3
Expanding the negative sign:
-3x + 2 = 3
Subtracting 2 from both sides:
-3x = 1
Dividing both sides by -3:
x = -1/3
Therefore, the solutions to the equation are x = 5/3 and x = -1/3.

d) 23 - 3|7x-1| = 2
To solve this equation, we need to isolate the absolute value term.
First, we subtract 23 from both sides of the equation:
-3|7x-1| = -21
Next, we divide both sides by -3:
|7x-1| = 7
Now, we have two cases to consider:
1) 7x-1 = 7
Solving for x, we add 1 to both sides:
7x = 8
Dividing both sides by 7:
x = 8/7
2) -(7x-1) = 7
Expanding the negative sign:
-7x + 1 = 7
Subtracting 1 from both sides:
-7x = 6
Dividing both sides by -7:
x = -6/7
Therefore, the solutions to the equation are x = 8/7 and x = -6/7.