To solve the equation \( 2x - 5 = 3(4x + 5) \), we will follow the steps outlined.
Step 1: Distributive Property
We need to apply the distributive property on the right side of the equation.
\[ 3(4x + 5) = 3 \cdot 4x + 3 \cdot 5 = 12x + 15 \]
Now, the equation becomes: \[ 2x - 5 = 12x + 15 \]
Step 2: Move variables to one side of the equation
To move the variable terms to one side, we will subtract \(12x\) from both sides of the equation using the addition/subtraction property of equalities.
\[ 2x - 12x - 5 = 15 \]
Combining like terms: \[ -10x - 5 = 15 \]
Step 3: Move constant to the other side of the equation
Next, we need to get the constants by themselves on one side. We can add \(5\) to both sides:
\[ -10x - 5 + 5 = 15 + 5 \]
This simplifies to: \[ -10x = 20 \]
Step 4: Isolate your variable
Finally, we will isolate \(x\) by dividing both sides of the equation by \(-10\) using the multiplication/division property of equalities.
\[ x = \frac{20}{-10} \]
This further simplifies to: \[ x = -2 \]
Conclusion:
The solution to the equation \(2x - 5 = 3(4x + 5)\) is:
\[ \boxed{-2} \]
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