Solve for x: 2x + 4(2x + 7) = 3(2x + 4).  solve this math quotation for me be specific

Let's solve the equation step by step:

### Problem
\[ 2x + 4(2x + 7) = 3(2x + 4) \]

### Step 1: Distribute the Constants
First, distribute the constants inside the parentheses.

\[ 2x + 4 \cdot 2x + 4 \cdot 7 = 3 \cdot 2x + 3 \cdot 4 \]

This simplifies to:

\[ 2x + 8x + 28 = 6x + 12 \]

### Step 2: Combine Like Terms
Next, combine the like terms on both sides of the equation.

On the left side:
\[ 2x + 8x = 10x \]

So, the equation becomes:

\[ 10x + 28 = 6x + 12 \]

### Step 3: Isolate the Variable Term
Subtract \( 6x \) from both sides to move the \( x \) terms to one side.

\[ 10x - 6x + 28 = 12 \]

This simplifies to:

\[ 4x + 28 = 12 \]

### Step 4: Solve for x
Now, subtract 28 from both sides to isolate the \( x \) term.

\[ 4x = 12 - 28 \]

\[ 4x = -16 \]

Finally, divide both sides by 4 to solve for \( x \).

\[ x = \frac{-16}{4} \]

\[ x = -4 \]

### Final Answer
The solution is \( x = -4 \).

Would you like further details or have any questions? 

Here are five related questions you might find helpful:

1. How would the solution change if the equation was \( 2x + 5(2x + 7) = 3(2x + 4) \)?
2. What is the solution if the equation was \( 3x + 4(2x + 9) = 5(2x + 1) \)?
3. Can you solve \( 2(x + 3) + 4(2x + 7) = 3(3x + 4) \) using the same steps?
4. What happens if you substitute \( x = -4 \) back into the original equation? Does it satisfy the equation?
5. How do you solve the equation \( 4(2x + 3) - 2(3x + 5) = 6 \)?

**Tip:** Always simplify each side of an equation as much as possible before moving terms across the equals sign. This reduces the chance of making mistakes.

Learn how to solve the equation 2x + 4(2x + 7) = 3(2x + 4) step by step with detailed explanations and examples. This problem involves algebraic equations, distributive property, and combining like terms. Suitable for Grades 7-9 students.

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