a) | x - 1/2 | = 0

Since the absolute value of any number is always non-negative, the only way for the absolute value to equal zero is if the expression inside the absolute value is equal to zero.

So, x - 1/2 = 0

Solving for x, we add 1/2 to both sides:

x = 1/2

Therefore, the solution to the equation | x - 1/2 | = 0 is x = 1/2.

b) | 2x + 1 | = 1

There are two possible cases to consider when dealing with absolute value equations.

Case 1: 2x + 1 = 1

Solving for x, we subtract 1 from both sides:

2x = 0

Dividing both sides by 2:

x = 0

Case 2: -(2x + 1) = 1

Solving for x, we distribute the negative sign:

-2x - 1 = 1

Adding 1 to both sides:

-2x = 2

Dividing both sides by -2:

x = -1

Therefore, the solutions to the equation | 2x + 1 | = 1 are x = 0 and x = -1.

c) 3 - 2 | x + 1 | = 1

First, we isolate the absolute value term by subtracting 3 from both sides:

-2 | x + 1 | = -2

Dividing both sides by -2:

| x + 1 | = 1

Again, there are two possible cases to consider.

Case 1: x + 1 = 1

Solving for x, we subtract 1 from both sides:

x = 0

Case 2: -(x + 1) = 1

Solving for x, we distribute the negative sign:

-x - 1 = 1

Adding 1 to both sides:

-x = 2

Multiplying both sides by -1:

x = -2

Therefore, the solutions to the equation 3 - 2 | x + 1 | = 1 are x = 0 and x = -2.