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To solve the equation \( |9x + 6| = 8 \), we need to consider the absolute value property, which states that \( |A| = B \) implies \( A = B \) or \( A = -B \).

### Step 1: Set up two separate equations
1. \( 9x + 6 = 8 \)
2. \( 9x + 6 = -8 \)

### Step 2: Solve each equation

**For \( 9x + 6 = 8 \):**
\[
9x = 8 - 6
\]
\[
9x = 2
\]
\[
x = \frac{2}{9}
\]

**For \( 9x + 6 = -8 \):**
\[
9x = -8 - 6
\]
\[
9x = -14
\]
\[
x = -\frac{14}{9}
\]

### Step 3: Solution
The solutions to the equation are:
\[
x = \frac{2}{9} \text{ and } x = -\frac{14}{9}
\]

So, the answer is:
**A.** The solutions are \( x = \frac{2}{9}, -\frac{14}{9} \).

Would you like further details or have any questions?

Here are five related questions for practice:
1. How do you solve an absolute value equation with multiple terms inside the absolute value?
2. How would the solution change if the equation were \( |9x + 6| = -8 \)?
3. Can you have no solution for an absolute value equation? If so, when?
4. What would the solution be if the equation was \( |9x + 6| = 0 \)?
5. How would you graph the solutions to \( |9x + 6| = 8 \)?

**Tip:** Remember, absolute values represent distance, so they can never be negative.

Find the real solutions of the equation |9x + 6| = 8.

Learn how to solve the absolute value equation |9x + 6| = 8 with a detailed step-by-step solution. This problem explores key algebraic concepts related to absolute value and linear equations, ideal for students in Grades 8-10.

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