The equation provided is:

$2x - (5x - 3) = -3(2x + 4)$

Let's solve for $x$.

Step 1: Simplify both sides of the equation

Start by distributing the negative sign on the left-hand side and the $-3$ on the right-hand side:

$2x - 5x + 3 = -6x - 12$

Step 2: Combine like terms

Simplify the equation by combining like terms on the left side:

$-3x + 3 = -6x - 12$

Step 3: Move all $x$-terms to one side and constants to the other side

Add $6x$ to both sides to get all $x$-terms on the left:

$-3x + 6x + 3 = -12$

This simplifies to:

$3x + 3 = -12$

Now, subtract 3 from both sides:

$3x = -15$

Step 4: Solve for $x$

Divide both sides by 3:

$x = -5$

Conclusion:

The value of $x$ that makes the equation true is $x = -5$.

Would you like more details on this process or have any questions?

Here are 5 related questions to explore:

1. How would the solution change if the equation were $2x - (5x + 3) = -3(2x + 4)$?
2. What is the graphical representation of the equation before solving for $x$?
3. How can this method be applied to similar linear equations?
4. What would the result be if you changed the sign on the $-3(2x + 4)$ term?
5. Can we solve this using substitution or another algebraic method?

Tip: Always double-check your distribution and combination of like terms to avoid small mistakes in algebraic manipulations.