Let's solve the linear equation step by step:

The equation is: $7x - 3(2x - 4) + 5 = 2(4x + 1) - 9$

Step 1: Expand both sides

Distribute the terms inside the parentheses on both sides.

Left-hand side: $7x - 3(2x - 4) + 5 = 7x - 6x + 12 + 5$ Simplify: $7x - 6x + 12 + 5 = x + 17$

Right-hand side: $2(4x + 1) - 9 = 8x + 2 - 9$ Simplify: $8x - 7$

So, the equation becomes: $x + 17 = 8x - 7$

Step 2: Move all the $x$-terms to one side and the constants to the other side

Subtract $x$ from both sides: $17 = 7x - 7$ Now add 7 to both sides: $24 = 7x$

Step 3: Solve for $x$

Divide both sides by 7: $x = \frac{24}{7}$

Thus, the solution is: $x = \frac{24}{7}$

Let me know if you'd like further details or clarifications!

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Here are 5 related questions:

1. How can we check if $x = \frac{24}{7}$ is the correct solution?
2. Can we solve this equation using a graphical method?
3. What if the equation had fractions? How would the steps differ?
4. How do we interpret the solution of a linear equation on a number line?
5. What happens if both sides of the equation simplify to the same expression?

Tip: Always simplify both sides of the equation first before isolating the variable!