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To solve the given equation \( |2x + 2| = 10 \), let's break it down.

### Step 1: Remove the absolute value
The absolute value equation \( |2x + 2| = 10 \) means that the expression inside the absolute value, \( 2x + 2 \), could either be equal to \( 10 \) or \( -10 \). So we split it into two cases:

1. \( 2x + 2 = 10 \)
2. \( 2x + 2 = -10 \)

### Step 2: Solve each case

**Case 1:**
\[
2x + 2 = 10
\]
Subtract 2 from both sides:
\[
2x = 8
\]
Divide by 2:
\[
x = 4
\]

**Case 2:**
\[
2x + 2 = -10
\]
Subtract 2 from both sides:
\[
2x = -12
\]
Divide by 2:
\[
x = -6
\]

### Step 3: Final answer
The solutions are \( x = 4 \) and \( x = -6 \).

### Step 4: Check the answer choices
The correct answer is **C**: \( x = 4 \) and \( x = -6 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do we handle absolute value equations with more complex expressions?
2. Can absolute value equations ever have no solution?
3. How do we solve inequalities involving absolute values?
4. What happens if the right side of the absolute value equation is negative?
5. How can we graph absolute value equations?

**Tip**: Always remember that an absolute value equation \( |A| = B \) only has real solutions when \( B \geq 0 \).

Learn how to solve the absolute value equation |2x + 2| = 10 step-by-step, involving splitting the equation into two cases and solving for x. Suitable for students in Grades 7-9.

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