Let's solve the equation \(2x - 5 = 3(4x + 5)\) step by step according to your instructions.
### Step 1: Distributing Property
We'll start by distributing \(3\) on the right side of the equation:
\[
2x - 5 = 3(4x) + 3(5)
\]
\[
2x - 5 = 12x + 15
\]
### Step 2: Move Variables to One Side of the Equation
Next, we want to move all the \(x\) terms to one side. We'll choose to subtract \(12x\) from both sides:
\[
2x - 5 - 12x = 12x + 15 - 12x
\]
\[
2x - 12x - 5 = 15
\]
\[
-10x - 5 = 15
\]
### Step 3: Move Constants to the Other Side of the Equation
Now, we will add \(5\) to both sides to isolate the term with \(x\):
\[
-10x - 5 + 5 = 15 + 5
\]
\[
-10x = 20
\]
### Step 4: Isolate Your Variable (Creation/Division of Properties)
Finally, we will divide both sides by \(-10\) to solve for \(x\):
\[
x = \frac{20}{-10}
\]
\[
x = -2
\]
### Conclusion
The solution to the equation \(2x - 5 = 3(4x + 5)\) is:
\[
\boxed{-2}
\]
If you have any further questions or need additional explanations, feel free to ask!