To solve the equation \( 2x - 5 = 3(4x + 5) \), follow these steps:
Step 1: Expand the right side of the equation
Distribute \( 3 \) on the right-hand side:
\[ 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \]
So, the equation becomes:
\[ 2x - 5 = 12x + 15 \]
Step 2: Move the \( x \) terms to one side
To do this, we can subtract \( 2x \) from both sides of the equation:
\[ 2x - 2x - 5 = 12x - 2x + 15 \]
This simplifies to:
\[ -5 = 10x + 15 \]
Step 3: Move the constant terms to the opposite side
Next, subtract \( 15 \) from both sides:
\[ -5 - 15 = 10x + 15 - 15 \]
This simplifies to:
\[ -20 = 10x \]
Step 4: Solve for \( x \)
Now, we can divide both sides by \( 10 \):
\[ x = \frac{-20}{10} \]
This simplifies to:
\[ x = -2 \]
Step 5: Verify the solution
To ensure our solution is correct, substitute \( x = -2 \) back into the original equation:
Starting with the left side:
\[ 2(-2) - 5 = -4 - 5 = -9 \]
Now let's evaluate the right side using \( x = -2 \):
\[ 3(4(-2) + 5) = 3(-8 + 5) = 3(-3) = -9 \]
Both sides equal \(-9\), so the equation holds true.
Final Answer:
The solution to the equation \( 2x - 5 = 3(4x + 5) \) is
\[ \boxed{-2} \]