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Let's solve the equation step by step.

The given equation is:

\[
16 = \frac{1}{2} (7x - 6)
\]

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 2 to get rid of the fraction:

\[
2 \times 16 = 2 \times \frac{1}{2} (7x - 6)
\]

This simplifies to:

\[
32 = 7x - 6
\]

### Step 2: Isolate the variable term
Add 6 to both sides of the equation:

\[
32 + 6 = 7x
\]

This gives:

\[
38 = 7x
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 7:

\[
x = \frac{38}{7}
\]

So, the solution in simplest form is:

\[
x = \frac{38}{7}
\]

Would you like further details or have any questions about this solution?

### Related Questions:
1. How do you simplify an equation with fractions?
2. What is the significance of isolating the variable in an equation?
3. How do you multiply both sides of an equation correctly?
4. How would you solve an equation with multiple fractions?
5. What happens if the variable appears on both sides of the equation?

**Tip**: Always try to eliminate fractions early in solving equations to make the process easier.

Solve for x in simplest form. 16 = (1/2)(7x - 6)

Learn how to solve the linear equation 16 = (1/2)(7x - 6) with a detailed step-by-step solution. This problem covers algebraic concepts, such as solving equations with fractions, and is suitable for students in Grades 7-9.

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