The given expression is:

\[
6\left(\dfrac{1}{2}w - \dfrac{3}{4}\right)
\]

Let's simplify this step by step:

1. **Distribute the 6** to both terms inside the parentheses:

\[
6 \times \dfrac{1}{2}w - 6 \times \dfrac{3}{4}
\]

2. **Simplify each term**:

- \( 6 \times \dfrac{1}{2}w = 3w \)
- \( 6 \times \dfrac{3}{4} = \dfrac{18}{4} = 4.5 \)

3. Therefore, the simplified expression is:

\[
3w - 4.5
\]

Let me know if you want more details on the steps or have any questions!

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Here are five related questions you could explore:

1. How would you simplify \( 5\left(\dfrac{2}{3}x + \dfrac{1}{6}\right) \)?
2. What happens if you add 4 to both sides of the equation \( 3w - 4.5 = 0 \)?
3. How would you solve \( 3w - 4.5 = 12 \) for \( w \)?
4. What is the result of simplifying \( 8\left(\dfrac{3}{4}x - 1\right) \)?
5. How would you factor the expression \( 3w - 4.5 \)?

**Tip:** When distributing a constant over a fraction, multiply the constant by the numerator and then divide by the denominator for easier calculations.

6\left(\dfrac{1}{2}w - \dfrac{3}{4}\right)

Learn how to simplify the algebraic expression 6(1/2w - 3/4) using the distributive property. This problem covers key concepts in algebra, including distribution and arithmetic with fractions. Suitable for students in Grades 6-8.

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