Let's solve the absolute value equation \( |-4g - 2| = 10 \).

### Step 1: Break the equation into two cases
The absolute value equation \( |A| = B \) implies two cases:
1. \( A = B \)
2. \( A = -B \)

For this equation, \( A = -4g - 2 \) and \( B = 10 \).

#### Case 1:
\[
-4g - 2 = 10
\]
Solve for \( g \):
\[
-4g = 10 + 2 = 12
\]
\[
g = \frac{12}{-4} = -3
\]

#### Case 2:
\[
-4g - 2 = -10
\]
Solve for \( g \):
\[
-4g = -10 + 2 = -8
\]
\[
g = \frac{-8}{-4} = 2
\]

### Step 2: Final solutions
The solutions are:
\[
g = -3 \quad \text{or} \quad g = 2
\]

Would you like more details on any part of the solution, or have any questions?

### Related questions:
1. How do you solve absolute value inequalities?
2. What is the difference between absolute value equations and inequalities?
3. Can absolute value equations have no solutions?
4. How do you solve equations with multiple absolute value expressions?
5. How can absolute value functions be graphed?

**Tip:** Always check if the solutions satisfy the original equation by substituting them back!

Learn how to solve the absolute value equation |-4g - 2| = 10 step-by-step. This solution breaks the equation into two cases, solves for g, and covers key concepts in algebra. Suitable for students in Grades 8-10.

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