Final answer:
The equation simplifies to 'w = -8' after combining like terms, subtracting '6w' and '29' from both sides, and finally dividing by 7.
Step-by-step explanation:
To solve the equation 18w - 5w + 29 = 6w - 27, we first simplify both sides of the equation by combining like terms. On the left side, we combine the terms with 'w' and on the right side, we're left with just '6w - 27' as it is already simplified.
Combining like terms on the left, we get: 13w + 29.
Now, we have 13w + 29 = 6w - 27. To solve for 'w', we subtract '6w' from both sides, which gives us 7w + 29 = -27. Next, we subtract '29' from both sides to get the term with 'w' by itself, resulting in 7w = -56. Finally, we divide both sides by 7 to isolate 'w', yielding w = -8.