1. State the problem. Solve for $w$ in the equation $5w + 9 = 39$. 2. Formula and rules. For a linear equation $ax + b = c$ you isolate the variable by subtracting $b$ from both sides and then dividing by $a$. Formula: $ax + b = c \Rightarrow ax = c - b \Rightarrow x = \frac{c - b}{a}$. Important rule: perform the same operation on both sides of the equation to maintain equality. 3. Step-by-step solution. Subtract 9 from both sides to isolate the term containing $w$. $5w + \cancel{9} - \cancel{9} = 39 - 9$. This simplifies to $5w = 30$. Divide both sides by 5 to solve for $w$. $\frac{\cancel{5}w}{\cancel{5}} = \frac{30}{5}$. Therefore $w = 6$. 4. Final answer. $w = 6$.