The equation given is:

\[
5 + 2|2x + 4| = 9
\]

Let's solve it step by step.

### Step 1: Isolate the absolute value expression

First, subtract 5 from both sides to isolate the absolute value term:

\[
2|2x + 4| = 9 - 5
\]

\[
2|2x + 4| = 4
\]

### Step 2: Divide by 2

Next, divide both sides of the equation by 2:

\[
|2x + 4| = \frac{4}{2}
\]

\[
|2x + 4| = 2
\]

### Step 3: Solve the absolute value equation

The absolute value equation \( |2x + 4| = 2 \) means there are two possible cases:

#### Case 1: \( 2x + 4 = 2 \)
Solve for \( x \):

\[
2x + 4 = 2
\]
\[
2x = 2 - 4
\]
\[
2x = -2
\]
\[
x = \frac{-2}{2} = -1
\]

#### Case 2: \( 2x + 4 = -2 \)
Solve for \( x \):

\[
2x + 4 = -2
\]
\[
2x = -2 - 4
\]
\[
2x = -6
\]
\[
x = \frac{-6}{2} = -3
\]

### Step 4: Final solution

The two solutions are:
\[
x = -1 \quad \text{or} \quad x = -3
\]

Would you like more details on any part of this solution?

### 5 Related Questions:
1. How do you solve absolute value equations with more complex expressions?
2. What happens if an absolute value equation has no solution?
3. Can absolute values affect inequalities differently?
4. How do you graph equations involving absolute values?
5. How do you check solutions in absolute value equations?

### Tip:
Always remember that absolute value equations have two cases: one positive and one negative, so solving them involves considering both possibilities.

Learn how to solve the absolute value equation 5 + 2|2x + 4| = 9 with a detailed, step-by-step solution. This problem focuses on isolating absolute value expressions and solving linear equations, suitable for students in Grades 8-10.

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