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The image contains a math problem asking to solve the equation \( |6x + 5| + 2 = 7 \).

Let's go through the steps to solve this equation:

1. **Isolate the absolute value expression:**

   \[
   |6x + 5| + 2 = 7
   \]

   Subtract 2 from both sides:

   \[
   |6x + 5| = 5
   \]

2. **Set up two separate equations:**

   Since the absolute value of an expression equals 5, the expression inside the absolute value can be either 5 or -5.

   \[
   6x + 5 = 5 \quad \text{or} \quad 6x + 5 = -5
   \]

3. **Solve each equation:**

   For \( 6x + 5 = 5 \):

   \[
   6x = 0
   \]
   \[
   x = 0
   \]

   For \( 6x + 5 = -5 \):

   \[
   6x = -10
   \]
   \[
   x = -\frac{10}{6} = -\frac{5}{3}
   \]

4. **Final Answer:**

   The solutions are \( x = 0 \) and \( x = -\frac{5}{3} \).

Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. How do you solve absolute value inequalities?
2. What happens when the equation inside the absolute value results in a negative number?
3. Can absolute value equations have no solution?
4. How would you solve \( |2x - 3| = 7 \)?
5. What is the general approach to solving equations involving absolute values?

**Tip:** When solving absolute value equations, always remember to consider both the positive and negative scenarios.

Step-by-step solution to the absolute value equation |6x + 5| + 2 = 7. Learn how to isolate the absolute value expression, split into linear equations, and find the solutions. Suitable for students in Grades 8-10.

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