To solve the equation \(2x - 5 = 3(4x + 5)\) using the specified steps, let's go through each step in detail.
Step 1: Distributive Property
We need to apply the distributive property to the right side of the equation:
\[ 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \]
Now, substitute this back into the equation:
\[ 2x - 5 = 12x + 15 \]
Step 2: Move variables to one side of the equation
Next, we will move the variable terms so that all terms involving \(x\) are on one side of the equation. Subtract \(12x\) from both sides:
\[ 2x - 12x - 5 = 15 \] This simplifies to:
\[ -10x - 5 = 15 \]
Step 3: Move constant to the other side of the equation
Now, we will move the constant term to the other side by adding \(5\) to both sides:
\[ -10x - 5 + 5 = 15 + 5 \] This simplifies to:
\[ -10x = 20 \]
Step 4: Isolate your variable
To isolate \(x\), we will divide both sides by \(-10\):
\[ x = \frac{20}{-10} \] This simplifies to:
\[ x = -2 \]
Final Answer
The solution to the equation \(2x - 5 = 3(4x + 5)\) is:
\[ \boxed{-2} \]