To solve the equation $|2x - 1| = 5$, we need to consider two possible cases for the absolute value:

Case 1: $2x - 1 = 5$

Solve for $x$: $2x - 1 = 5$ Add 1 to both sides: $2x = 6$ Divide both sides by 2: $x = 3$

Case 2: $2x - 1 = -5$

Solve for $x$: $2x - 1 = -5$ Add 1 to both sides: $2x = -4$ Divide both sides by 2: $x = -2$

Conclusion:

The two solutions to the equation $|2x - 1| = 5$ are $x = 3$ and $x = -2$.

Thus, there are 2 solutions.

Would you like a more detailed explanation of absolute value equations or have any other questions?

Here are some related questions:

1. How do you solve absolute value equations with a negative value on the right-hand side?
2. What is the meaning of an absolute value function graphically?
3. How do absolute value equations change when there are multiple terms inside the absolute value?
4. How do you solve absolute value inequalities?
5. How can you apply absolute value equations in real-world problems?

Tip: Always split the absolute value equation into two separate equations—one for the positive value and one for the negative value.