Let's start from the equation you provided:
\[ \frac{6x - 10}{2} = 7x + 15 \]
First, to eliminate the fraction, multiply both sides by 2:
\[ 6x - 10 = 2(7x + 15) \]
Now simplify the right side:
\[ 6x - 10 = 14x + 30 \]
Next, subtract \(3x\) from each side as you instructed. We will first rearrange the equation to have \(x\) terms on one side:
\[ 6x - 10 - 3x = 14x + 30 - 3x \]
This simplifies to:
\[ (6x - 3x) - 10 = (14x - 3x) + 30 \]
That leads us to:
\[ 3x - 10 = 11x + 30 \]
Now we can isolate \(x\) by completing the equation. We will subtract \(11x\) from both sides:
\[ 3x - 11x - 10 = 30 \]
This simplifies to:
\[ -8x - 10 = 30 \]
Next, add 10 to both sides:
\[ -8x = 40 \]
Now divide by \(-8\):
\[ x = -5 \]
So, the solution to the equation is:
\[ x = -5 \]
1 answer