To solve the equation \( 10 + 10x = 30 + 5x - 5x - 5x \), we first simplify the right side:
- Combine the like terms on the right: \[ 30 + 5x - 5x - 5x = 30 + (5x - 5x - 5x) \] This simplifies to: \[ 30 - 5x \]
Now our equation looks like: \[ 10 + 10x = 30 - 5x \]
Next, we can get all terms involving \( x \) on one side and constant terms on the other side. Start by adding \( 5x \) to both sides: \[ 10 + 10x + 5x = 30 - 5x + 5x \] This simplifies to: \[ 10 + 15x = 30 \]
Now, subtract \( 10 \) from both sides to isolate the terms with \( x \): \[ 15x = 30 - 10 \] This simplifies to: \[ 15x = 20 \]
Now, divide both sides by \( 15 \) to solve for \( x \): \[ x = \frac{20}{15} = \frac{4}{3} \]
So the solution is: \[ \boxed{\frac{4}{3}} \]