To solve the equation:

\[
|3x - 5| - 6 = 4
\]

1. **Isolate the absolute value** term by adding 6 to both sides:
   \[
   |3x - 5| = 10
   \]

2. **Set up two separate equations** because the expression inside the absolute value can be either positive or negative:
   \[
   3x - 5 = 10 \quad \text{or} \quad 3x - 5 = -10
   \]

3. **Solve each equation** separately:

   - For \(3x - 5 = 10\):
     \[
     3x = 15
     \]
     \[
     x = 5
     \]

   - For \(3x - 5 = -10\):
     \[
     3x = -5
     \]
     \[
     x = -\frac{5}{3}
     \]

4. **Final solution**:
   \[
   x = 5 \quad \text{or} \quad x = -\frac{5}{3}
   \]

So, the values of \( x \) that satisfy the equation are:

\[
x = 5 \quad \text{or} \quad x = -\frac{5}{3}
\]

Would you like more details on any of the steps?

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Here are 5 related questions:
1. What is the solution if the absolute value equation were \( |3x - 5| + 6 = 4 \)?
2. How would the solution change if we had \( |3x - 5| = 10x \)?
3. What are the steps to solve \( |2x + 4| = 8 \)?
4. Can absolute value equations have no solutions? If so, under what conditions?
5. How do you solve absolute value inequalities, like \( |2x - 1| < 5 \)?

**Tip:** When solving absolute value equations, always isolate the absolute value expression before setting up separate equations.

Learn how to solve the absolute value equation |3x - 5| - 6 = 4 step by step. This solution covers algebraic techniques, including isolating the absolute value, setting up two linear equations, and solving for x. Suitable for students in Grades 8-10.

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