To solve the equation \( 12w - 27 = -15w - 34 + 14w \), first, simplify the right side.
Combine the terms involving \( w \): \[ -15w + 14w = -1w \] Now the equation becomes: \[ 12w - 27 = -1w - 34 \]
Next, add \( 1w \) to both sides to get all the \( w \) terms on one side: \[ 12w + 1w - 27 = -34 \] This simplifies to: \[ 13w - 27 = -34 \]
Now, add 27 to both sides to isolate the \( w \) term: \[ 13w = -34 + 27 \] This simplifies to: \[ 13w = -7 \]
Finally, divide both sides by 13 to solve for \( w \): \[ w = \frac{-7}{13} \]
So, the solution is: \[ w = -\frac{7}{13} \]