Let's solve the equation step by step:

### Given equation:
\[
3(2x + 9) + \frac{1}{2}(4x - 8) = 55
\]

### Step 1: Expand the brackets.
\[
3(2x + 9) = 6x + 27
\]
\[
\frac{1}{2}(4x - 8) = 2x - 4
\]
Now the equation becomes:
\[
6x + 27 + 2x - 4 = 55
\]

### Step 2: Combine like terms.
\[
6x + 2x + 27 - 4 = 55
\]
\[
8x + 23 = 55
\]

### Step 3: Subtract 23 from both sides.
\[
8x = 55 - 23
\]
\[
8x = 32
\]

### Step 4: Divide both sides by 8.
\[
x = \frac{32}{8} = 4
\]

### Solution:
\[
x = 4
\]

Would you like further details or explanations? Here are some related questions:

1. How do you verify solutions to linear equations?
2. Can you solve a similar equation with fractions on both sides?
3. What happens when there's no solution to an equation?
4. How do you deal with variables on both sides of the equation?
5. Can you explain how the distributive property works in more detail?

**Tip:** Always double-check your work by substituting the solution back into the original equation.

Learn how to solve the linear equation 3(2x + 9) + 1/2(4x - 8) = 55 with a detailed step-by-step breakdown. This problem covers algebraic concepts such as the distributive property, combining like terms, and solving for x. Suitable for students in Grades 8-10.

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