To solve the equation \(\left|\frac{7a + 8}{6}\right| = 2\), we need to consider the properties of absolute value. The equation \(\left|x\right| = 2\) implies that either:

\[
\frac{7a + 8}{6} = 2 \quad \text{or} \quad \frac{7a + 8}{6} = -2
\]

Let's solve both cases:

### Case 1: \(\frac{7a + 8}{6} = 2\)

1. Multiply both sides by 6 to eliminate the fraction:
   \[
   7a + 8 = 12
   \]
2. Subtract 8 from both sides:
   \[
   7a = 4
   \]
3. Divide both sides by 7:
   \[
   a = \frac{4}{7}
   \]

### Case 2: \(\frac{7a + 8}{6} = -2\)

1. Multiply both sides by 6:
   \[
   7a + 8 = -12
   \]
2. Subtract 8 from both sides:
   \[
   7a = -20
   \]
3. Divide both sides by 7:
   \[
   a = \frac{-20}{7}
   \]

### Final Answer:
The solutions are:
\[
a = \frac{4}{7} \quad \text{or} \quad a = \frac{-20}{7}
\]

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you solve absolute value equations with variables on both sides?
2. What happens if the absolute value is set to zero?
3. Can you graph the solutions of the equation on a number line?
4. How do you solve absolute value inequalities?
5. What are the properties of absolute values that are useful in solving equations?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy the absolute value condition.

Learn how to solve the absolute value equation |(7a + 8) / 6| = 2 with detailed step-by-step solutions. This problem involves operations with fractions and absolute value equations. Suitable for students in Grades 9-12.

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