Question

) $9a - \frac{1}{3}(9a - 18) = 39$

Explanation:

Step1: Distribute the fraction

First, we distribute the $\frac{1}{3}$ to the terms inside the parentheses. So, $\frac{1}{3}(9a - 18)$ becomes $\frac{1}{3} \times 9a - \frac{1}{3} \times 18$, which simplifies to $3a - 6$.
The equation now is $9a - (3a - 6) = 39$.

Step2: Remove parentheses

When we remove the parentheses, we have to distribute the negative sign. So, $9a - 3a + 6 = 39$.

Step3: Combine like terms

Combine the $9a$ and $-3a$ terms. $9a - 3a = 6a$, so the equation becomes $6a + 6 = 39$.

Step4: Subtract 6 from both sides

Subtract 6 from each side: $6a + 6 - 6 = 39 - 6$, which simplifies to $6a = 33$.

Step5: Solve for a

Divide both sides by 6: $a = \frac{33}{6}$, which simplifies to $a = \frac{11}{2}$ or $a = 5.5$.

Answer:

$a = \frac{11}{2}$ (or $a = 5.5$)