To solve the equation \( 2x - 5 = 3(4x + 5) \), we'll follow these steps:
Step 1: Expand the right side
First, we need to distribute the 3 on the right side of the equation:
\[ 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \]
Now we can rewrite the equation:
\[ 2x - 5 = 12x + 15 \]
Step 2: Move all terms involving \( x \) to one side
Next, we want to move all terms involving \( x \) to one side of the equation and constant terms to the other side. We can do this by subtracting \( 12x \) from both sides:
\[ 2x - 12x - 5 = 15 \]
This simplifies to:
\[ -10x - 5 = 15 \]
Step 3: Move the constants to the other side
Now, we can add 5 to both sides to isolate the term with \( x \):
\[ -10x - 5 + 5 = 15 + 5 \]
This simplifies to:
\[ -10x = 20 \]
Step 4: Solve for \( x \)
Now, we divide both sides by -10 to solve for \( x \):
\[ x = \frac{20}{-10} = -2 \]
Solution
Thus, the solution to the equation \( 2x - 5 = 3(4x + 5) \) is:
\[ \boxed{-2} \]
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