Let's solve the equation step by step:

\[
12w - 5 - 3w = 40
\]

### Step 1: Combine like terms
Group the terms with \( w \) on the left-hand side:

\[
(12w - 3w) - 5 = 40
\]

Simplifying:

\[
9w - 5 = 40
\]

### Step 2: Add 5 to both sides
To isolate the term with \( w \), add 5 to both sides:

\[
9w = 40 + 5
\]

\[
9w = 45
\]

### Step 3: Solve for \( w \)
Now, divide both sides by 9:

\[
w = \frac{45}{9}
\]

\[
w = 5
\]

So, the solution is \( w = 5 \).

Do you need more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What happens if you have an equation like \( 15w - 7 + 2w = 53 \)?
2. How would you solve \( 9w + 4 = 2w + 25 \)?
3. What if you had to solve an equation with a fraction, such as \( \frac{7w}{2} - 3 = 10 \)?
4. How does solving an inequality differ from solving an equation like this?
5. How do you solve a quadratic equation, like \( w^2 - 4w - 5 = 0 \)?

**Tip:** Always try to simplify both sides of an equation as much as possible before isolating the variable.

Learn how to solve the linear equation 12w – 5 – 3w = 40 with a clear step-by-step explanation. This problem focuses on key algebraic skills, such as combining like terms and isolating variables, suitable for students in Grades 6-8.

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