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.