Question

multiply both sides of the equation by 3 to solve for the value of b.
\\(\frac{2}{3}b + 9\\) = \\(b + 11\\)
\\(-\frac{2}{3}b\\) = \\(-\frac{2}{3}b\\)
9 = \\(\frac{1}{3}b + 11\\)
-11 = -11
-2 = \\(\frac{1}{3}b\\)
3·(-2) = 3·(\\(\frac{1}{3}b\\))
\\(\square\\) = \\(\square\\)

Explanation:

Step1: Start with original equation

$\frac{2}{3}b + 9 = b + 11$

Step2: Multiply all terms by 3

$3 \cdot \frac{2}{3}b + 3 \cdot 9 = 3 \cdot b + 3 \cdot 11$

Step3: Simplify each term

$2b + 27 = 3b + 33$

Step4: Isolate b terms (subtract 2b)

$27 = b + 33$

Step5: Solve for b (subtract 33)

$b = 27 - 33$

Answer:

$b = -6$

To fill the final empty box in the provided work:
The last step shows $3 \cdot (-2) = 3 \cdot \frac{1}{3}b$, which simplifies to $\boldsymbol{-6 = b}$ (matching the solved value).