Let's follow the steps described in your prompt to solve the equation.
You have the following equation before the adjustments:
\[ 2s - 10 = -3s - 8 + 3s + 3s \]
First, let's simplify the right side:
\[ -3s + 3s + 3s = 3s - 8 \]
So now the equation looks like this:
\[ 2s - 10 = 3s - 8 \]
Now, let's eliminate \(-10\) on the left side by adding \(10\) to both sides:
\[ 2s - 10 + 10 = 3s - 8 + 10 \]
Which simplifies to:
\[ 2s = 3s + 2 \]
Next, we will rearrange the equation to isolate \(s\). We can subtract \(3s\) from both sides:
\[ 2s - 3s = 2 \]
This simplifies to:
\[ -s = 2 \]
To solve for \(s\), we multiply both sides by \(-1\):
\[ s = -2 \]
So the final solution is:
\[ s = -2 \]
The completed equation paths show:
\[ 2s = 3s + 2 \implies ? = ? \rightarrow 2s - 3s = 2 \implies -s = 2 \implies s = -2 \]