To solve the equation $|2x - 4| = 10$, we need to break it into two cases, as the absolute value can result in either a positive or negative expression.

Case 1: $2x - 4 = 10$

$2x - 4 = 10$ Add 4 to both sides: $2x = 14$ Now divide by 2: $x = 7$

Case 2: $2x - 4 = -10$

$2x - 4 = -10$ Add 4 to both sides: $2x = -6$ Now divide by 2: $x = -3$

Final Answer:

The solutions are $x = 7$ and $x = -3$.

Would you like further clarification on absolute value equations or more details on this solution?

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Here are 5 related questions:

1. How do you solve absolute value inequalities?
2. What is the graphical interpretation of absolute value equations?
3. How do you solve the equation $|3x + 5| = 8$?
4. What happens if the equation $|2x - 4| = -10$ is given instead?
5. Can you solve absolute value equations using a different method, like squaring?

Tip: When solving absolute value equations, always remember to consider both the positive and negative cases!