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.

Learn how to solve the inequality |10x - 6| < 4 with a detailed step-by-step solution. This problem covers key algebraic concepts such as absolute value inequalities and involves splitting the inequality into two cases. Suitable for students in Grades 8-10.

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