https://file.aiquickdraw.com/mathbot/file/1726385164593evsbyha1.jpg

The equation in the image is:

\[
\frac{3\left(\frac{5}{9}x + \frac{4}{27}\right)}{2} = 3
\]

Let's solve it step by step.

### Step 1: Eliminate the fraction by multiplying both sides by 2.
\[
3\left(\frac{5}{9}x + \frac{4}{27}\right) = 6
\]

### Step 2: Distribute the 3 across the terms inside the parentheses.
\[
3 \times \frac{5}{9}x + 3 \times \frac{4}{27} = 6
\]
\[
\frac{15}{9}x + \frac{12}{27} = 6
\]

### Step 3: Simplify the fractions.
\[
\frac{15}{9} = \frac{5}{3}, \quad \frac{12}{27} = \frac{4}{9}
\]
Now, the equation becomes:
\[
\frac{5}{3}x + \frac{4}{9} = 6
\]

### Step 4: Eliminate the fractions by multiplying through by 9 (the least common denominator).
\[
9 \times \left(\frac{5}{3}x + \frac{4}{9}\right) = 9 \times 6
\]
\[
3 \times 5x + 4 = 54
\]
\[
15x + 4 = 54
\]

### Step 5: Solve for \(x\).
\[
15x = 54 - 4
\]
\[
15x = 50
\]
\[
x = \frac{50}{15} = \frac{10}{3}
\]

Thus, the solution is:
\[
x = \frac{10}{3}
\]

Would you like further details or explanations on any steps?

### Related questions:
1. How do you handle equations with variables on both sides?
2. What happens if there are multiple fractions in the equation?
3. Can you demonstrate how to cross-multiply in a proportion equation?
4. How do you solve quadratic equations that contain fractions?
5. What is the best approach for solving systems of equations involving fractions?

**Tip:** When dealing with fractions in algebra, it's often useful to clear them early by multiplying both sides of the equation by the least common denominator.

Solve the equation: (3(5/9)x + 4/27)/2 = 3.

Learn how to solve the linear equation with fractions: (3(5/9)x + 4/27)/2 = 3. This detailed solution uses key algebraic concepts such as distributing terms and clearing fractions. Suitable for students in Grades 8-10.

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