We start with the equation:

\[
\frac{w - 5}{2} - 6 = \frac{w + 6}{3}
\]

### Step 1: Eliminate the fractions
To eliminate the fractions, multiply both sides of the equation by the least common denominator (LCD), which is 6. Multiply every term by 6:

\[
6 \times \left(\frac{w - 5}{2}\right) - 6 \times 6 = 6 \times \left(\frac{w + 6}{3}\right)
\]

Simplify each term:

\[
3(w - 5) - 36 = 2(w + 6)
\]

### Step 2: Expand both sides
Expand the terms on both sides:

\[
3w - 15 - 36 = 2w + 12
\]

Simplify:

\[
3w - 51 = 2w + 12
\]

### Step 3: Collect like terms
Move all terms involving \(w\) to one side and constants to the other side:

\[
3w - 2w = 12 + 51
\]

Simplify:

\[
w = 63
\]

Thus, the solution is \( w = 63 \).

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

Here are 5 related questions:
1. What happens if you change the constants in the equation?
2. How do you handle equations with different denominators?
3. What if the equation has variables on both sides with exponents?
4. Can you solve a similar equation involving square roots?
5. How do you check if your solution for \(w\) is correct?

**Tip:** Always start by eliminating fractions when solving equations—they simplify the problem significantly!

Learn how to solve the linear equation w-5/2 -6 = w+6/3 with detailed steps. This problem covers algebraic concepts, including eliminating fractions and balancing equations. Ideal for students in Grades 8-10.

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