To solve the inequality \(7|4a-6| < 42\), follow these steps:

1. **Divide both sides by 7** to simplify:
   \[
   |4a - 6| < \frac{42}{7}
   \]
   \[
   |4a - 6| < 6
   \]

2. **Set up the compound inequality**:
   Since \( |x| < c \) implies \( -c < x < c \), we have:
   \[
   -6 < 4a - 6 < 6
   \]

3. **Add 6 to each part of the inequality**:
   \[
   -6 + 6 < 4a - 6 + 6 < 6 + 6
   \]
   \[
   0 < 4a < 12
   \]

4. **Divide the entire inequality by 4** to solve for \(a\):
   \[
   \frac{0}{4} < \frac{4a}{4} < \frac{12}{4}
   \]
   \[
   0 < a < 3
   \]

So, the solution is \( 0 < a < 3 \).

Do you want more details, or have any questions?

Here are 5 related questions:
1. How would you solve \( 2|x - 5| \leq 10 \)?
2. What is the solution for \( |3x + 7| > 8 \)?
3. Can you solve \( 5|2y - 1| = 15 \)?
4. How would you approach \( |x + 4| - 2 > 5 \)?
5. How does the solution change if the inequality were \( 7|4a-6| \leq 42 \)?

**Tip:** Always remember that when solving absolute value inequalities, you create two separate inequalities to account for both the positive and negative cases.

This page provides a step-by-step solution to the inequality 7|4a-6|<42. Learn how to simplify the inequality, set up a compound inequality, and solve for the variable 'a'. Key concepts include algebra and absolute value properties. Suitable for students in Grades 9-10.

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