To solve the inequality $|10x - 6| < 4$, we need to break it down into two cases based on the definition of absolute value:

Case 1: $10x - 6 < 4$

$10x - 6 < 4$ Add 6 to both sides: $10x < 10$ Now, divide by 10: $x < 1$

Case 2: $-(10x - 6) < 4$, which simplifies to $10x - 6 > -4$

$10x - 6 > -4$ Add 6 to both sides: $10x > 2$ Now, divide by 10: $x > \frac{2}{10} = 0.2$

Final Solution:

The solution is the intersection of both conditions: $0.2 < x < 1$.

Thus, the solution to $|10x - 6| < 4$ is: $0.2 < x < 1$

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How would you solve $|10x - 6| = 4$?
2. What is the solution to $|10x - 6| > 4$?
3. How do absolute value inequalities change with different constants inside?
4. How can this solution be represented on a number line?
5. How do you handle absolute value inequalities involving quadratics?

Tip: Always check the range of possible solutions by splitting absolute value inequalities into two cases.