The equation we are working with is:

$|2x - 1| = 5$

To solve for $x$, we need to recall that the absolute value equation $|A| = B$ implies two possible cases:

1. $A = B$
2. $A = -B$

Step 1: Set up the two cases

Case 1: $2x - 1 = 5$

Solve for $x$:

$2x - 1 = 5$ $2x = 5 + 1$ $2x = 6$ $x = 3$

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

Solve for $x$:

$2x - 1 = -5$ $2x = -5 + 1$ $2x = -4$ $x = -2$

Step 2: Conclusion

The two solutions to the equation $|2x - 1| = 5$ are:

$x = 3 \quad \text{and} \quad x = -2$

Thus, the equation has two solutions.

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Would you like further details or have any questions about the steps?

Here are five related questions:

1. How would the solution change if the equation was $|2x - 1| = 4$?
2. What is the graphical representation of the equation $|2x - 1| = 5$?
3. How would you solve $|x + 3| = 7$?
4. What happens when you solve an equation with an absolute value on both sides, like $|x + 4| = |x - 1|$?
5. How does the concept of absolute value relate to real-world problems?

Tip: When solving absolute value equations, remember that the absolute value represents the distance of a number from zero on the number line, which leads to two possible cases: one positive and one negative.