Let's solve the equation step by step:

Given equation:
\[
7 + 2(12x - 4) = -4(3x + 1) - 5x
\]

### Step 1: Distribute the constants on both sides.
\[
7 + 2 \times 12x - 2 \times 4 = -4 \times 3x - 4 \times 1 - 5x
\]
\[
7 + 24x - 8 = -12x - 4 - 5x
\]

### Step 2: Simplify both sides by combining like terms.
\[
(24x - 1) = -17x - 4
\]

### Step 3: Move all terms involving \(x\) to one side and the constants to the other.
\[
24x + 17x = -4 + 1
\]
\[
41x = -3
\]

### Step 4: Solve for \(x\).
\[
x = \frac{-3}{41}
\]

So, the solution is:
\[
x = \frac{-3}{41}
\]

Would you like more details, or do you have any questions?

Here are some related questions:
1. How do you solve equations involving distributive properties?
2. What happens when you have variables on both sides of an equation?
3. How can you check if your solution to an equation is correct?
4. What is the importance of simplifying equations step by step?
5. How would this equation change if the constants were different?

**Tip:** Always double-check your work by substituting your solution back into the original equation to ensure it's correct.

Explore how to solve the linear equation 7 + 2(12x - 4) = -4(3x + 1) - 5x step-by-step. This problem involves understanding equations, applying distributive property, and simplifying expressions. Suitable for high school students.

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