To solve the equation \( |5x - 10| = 8 \), we'll need to consider the two possible cases for the absolute value.

### Case 1: \( 5x - 10 = 8 \)
\[
5x - 10 = 8
\]
Add 10 to both sides:
\[
5x = 18
\]
Divide both sides by 5:
\[
x = \frac{18}{5} = 3.6
\]

### Case 2: \( 5x - 10 = -8 \)
\[
5x - 10 = -8
\]
Add 10 to both sides:
\[
5x = 2
\]
Divide both sides by 5:
\[
x = \frac{2}{5} = 0.4
\]

### Final Answer
The solutions to the equation \( |5x - 10| = 8 \) are:
\[
x = 3.6 \quad \text{or} \quad x = 0.4
\]

Would you like more details or have any questions?

Here are some related questions for further practice:
1. Solve \( |3x + 7| = 5 \).
2. Solve \( |2x - 4| = 10 \).
3. Solve \( |7x + 2| = 14 \).
4. Solve \( |x - 6| = 3 \).
5. Solve \( |4x + 8| = 12 \).
6. Solve \( |6x - 3| = 9 \).
7. Solve \( |8x + 1| = 7 \).
8. Solve \( |9x - 5| = 11 \).

**Tip:** Always remember that absolute value equations have two cases, corresponding to the expression inside being either positive or negative.

Learn how to solve the equation |5x - 10| = 8 with detailed step-by-step solutions for both cases of the absolute value. This problem covers absolute value equations and linear equations, suitable for high school students.

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