### Instruction: Solve for $y$: $3y+7y = 282-8(y-3)$.### Response: To solve for $y$, I need to isolate it on one side of the equation by using inverse operations.
First, I can simplify the equation by combining like terms and expanding the brackets.
On the left side, $3y+7y$ is just $10y$.
On the right side, $282-8(y-3)$ is $282-8y+24$, which is $306-8y$.
So the equation becomes $10y = 306-8y$.
Next, I can add $8y$ to both sides to eliminate it from the right side.
This gives me $18y = 306$.
Then, I can divide both sides by $18$ to get $y$ by itself.
This gives me $y = 306/18$, which is $y = 17$.