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The problem asks you to find the value of the expression \( (4x - 12) + \left( \frac{1}{2}xy - 10 \right) \) for \( x = 4 \) and \( y = 6 \).

### Step 1: Substitute the given values \( x = 4 \) and \( y = 6 \) into the expression.

\[
(4x - 12) + \left( \frac{1}{2}xy - 10 \right)
\]

Substituting \( x = 4 \) and \( y = 6 \):

\[
(4(4) - 12) + \left( \frac{1}{2}(4)(6) - 10 \right)
\]

### Step 2: Simplify each part.

First part:
\[
4(4) - 12 = 16 - 12 = 4
\]

Second part:
\[
\frac{1}{2}(4)(6) = 12
\]
\[
12 - 10 = 2
\]

### Step 3: Add the two parts together.

\[
4 + 2 = 6
\]

Thus, the value of the expression is **6**.

Would you like further details or have any questions?

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Here are 5 related questions:
1. What would the value be if \( y = 8 \) instead of \( y = 6 \)?
2. How does distributing multiplication over addition help in simplifying such expressions?
3. What if the expression had an additional term \( + x^2 \)? How would the process change?
4. What role does the coefficient \( \frac{1}{2} \) play in adjusting the value of the expression?
5. How would this expression change if \( x \) or \( y \) were negative?

**Tip**: Always substitute values carefully, especially when dealing with fractions, to avoid calculation errors.

Find the value of the expression (4x − 12) + (1/2xy − 10) for x = 4 and y = 6.

Learn how to find the value of the expression (4x − 12) + (1/2xy − 10) for x = 4 and y = 6. This problem involves key algebraic concepts such as substitution and expression simplification. Suitable for students in Grades 6-8.

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