https://file.aiquickdraw.com/mathbot/file/1728756072447zo8b196g.jpg

Let's first solve the equation given in the image:

\[
\frac{1}{2}(x - 4) + 6 = 3x - 5
\]

### Step 1: Distribute the \(\frac{1}{2}\) on the left side:
\[
\frac{1}{2}(x - 4) = \frac{1}{2}x - 2
\]
So the equation becomes:
\[
\frac{1}{2}x - 2 + 6 = 3x - 5
\]

### Step 2: Simplify the constants on the left side:
\[
\frac{1}{2}x + 4 = 3x - 5
\]

### Step 3: Move all \(x\)-terms to one side and constants to the other:
\[
\frac{1}{2}x - 3x = -5 - 4
\]

### Step 4: Simplify both sides:
\[
-\frac{5}{2}x = -9
\]

### Step 5: Solve for \(x\):
\[
x = \frac{-9}{-\frac{5}{2}} = \frac{-9 \times 2}{-5} = \frac{18}{5}
\]

So, \(x = \frac{18}{5}\).

### Step 6: Find \(5 - x\):
\[
5 - x = 5 - \frac{18}{5} = \frac{25}{5} - \frac{18}{5} = \frac{7}{5}
\]

Thus, the value of \(5 - x\) is \(\frac{7}{5}\).

---

Would you like more details on any step?

Here are 5 related questions:
1. How can we verify if \(\frac{18}{5}\) is the correct solution for \(x\)?
2. What is the importance of isolating variables in equations?
3. How would the process change if the equation had fractions on both sides?
4. How can you solve equations involving higher powers of \(x\)?
5. What would happen if we mistakenly combined terms incorrectly?

**Tip:** When solving equations with fractions, it's helpful to eliminate the fractions early on by multiplying through by the denominator!

If x is the solution to the equation \(\frac{1}{2}(x - 4) + 6 = 3x - 5\), what is the value of 5 - x?

This problem demonstrates how to solve the equation \(\frac{1}{2}(x - 4) + 6 = 3x - 5\) and find the value of 5 - x. Learn the step-by-step solution involving distribution, combining like terms, and working with fractions. Suitable for students in Grades 9-10.

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