The equation you provided is:

\[
\frac{w - 5}{2} = 1 + \frac{w + 4}{8}
\]

Let's solve for \( w \).

### Step 1: Eliminate the fractions
Multiply the entire equation by 8 to eliminate the denominators:

\[
8 \times \left(\frac{w - 5}{2}\right) = 8 \times \left(1 + \frac{w + 4}{8}\right)
\]

Simplify:

\[
4(w - 5) = 8(1) + (w + 4)
\]

This becomes:

\[
4w - 20 = 8 + w + 4
\]

### Step 2: Combine like terms
Simplify the right-hand side:

\[
4w - 20 = w + 12
\]

### Step 3: Isolate \( w \)
Move all terms involving \( w \) to one side:

\[
4w - w = 12 + 20
\]

Simplify:

\[
3w = 32
\]

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

\[
w = \frac{32}{3}
\]

Thus, the solution is:

\[
w = \frac{32}{3}
\]

Would you like a breakdown of the steps or further details on the process?

Here are 5 related questions:
1. How would the solution change if the fractions were more complex?
2. What if we multiplied both sides of the equation by different values instead of 8?
3. How can we check if \( w = \frac{32}{3} \) satisfies the original equation?
4. How would the solution be different if we had additional terms in the equation?
5. How can we approach similar equations involving higher powers of \( w \)?

**Tip:** Always clear fractions first in equations to simplify the solving process.

Learn how to solve the linear equation w - 5/2 = 1 + (w + 4)/8 by eliminating fractions, simplifying terms, and isolating the variable. This problem covers key algebraic concepts suitable for students in Grades 8-10.

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