We are given the equation:

\[
\frac{1}{2}(x + 3) = 2(x - 3)
\]

### Step 1: Eliminate the fraction

Multiply both sides of the equation by 2 to eliminate the fraction:

\[
(x + 3) = 4(x - 3)
\]

### Step 2: Expand both sides

Expand both sides of the equation:

\[
x + 3 = 4x - 12
\]

### Step 3: Isolate the variable \(x\)

Move all terms involving \(x\) to one side and constant terms to the other side:

\[
x - 4x = -12 - 3
\]

Simplify:

\[
-3x = -15
\]

### Step 4: Solve for \(x\)

Divide both sides by \(-3\):

\[
x = \frac{-15}{-3} = 5
\]

Thus, the solution is:

\[
x = 5
\]

Would you like more details on any step, or do you have any questions?

### Relative Questions:
1. How can you check the solution of an equation?
2. How do you handle equations with multiple variables?
3. What is the difference between solving linear and quadratic equations?
4. How can you solve equations involving fractions?
5. What are the common mistakes when solving linear equations?

### Tip:
Always check your solution by plugging it back into the original equation to verify it works!

Learn how to solve the linear equation 1/2(x+3)=2(x-3) with a step-by-step solution. This problem covers essential algebraic concepts, including fraction elimination and variable isolation, suitable for students in Grades 7-8.

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