−1/2(8×14÷2+5−(6−∣−6∣) −7)

Let's solve the expression step by step:

\[
-\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - (6 - | -6 |) - 7 \right)
\]

### Step 1: Simplify inside the absolute value
The absolute value of \(-6\) is:
\[
| -6 | = 6
\]
So the expression becomes:
\[
-\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - (6 - 6) - 7 \right)
\]

### Step 2: Simplify inside the parentheses
\(6 - 6 = 0\), so:
\[
-\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - 0 - 7 \right) = -\frac{1}{2} \left( 8 \times 14 \div 2 + 5 - 7 \right)
\]

### Step 3: Perform multiplication and division
\[
8 \times 14 = 112, \quad 112 \div 2 = 56
\]
So the expression is now:
\[
-\frac{1}{2} \left( 56 + 5 - 7 \right)
\]

### Step 4: Simplify inside the parentheses
\[
56 + 5 - 7 = 54
\]
So the expression becomes:
\[
-\frac{1}{2} \times 54
\]

### Step 5: Perform the multiplication
\[
-\frac{1}{2} \times 54 = -27
\]

Thus, the value of the expression is:

\[
\boxed{-27}
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. What is the value of \(\frac{1}{3}(9 \times 6 - 4 + | -2 |)\)?
2. How do you evaluate expressions with absolute values?
3. How does the distributive property work in expressions like \(-\frac{1}{2}(a + b)\)?
4. What are the rules for performing operations inside parentheses first (PEMDAS)?
5. How does multiplying by a negative fraction affect the result?

**Tip:** Always solve expressions inside absolute values first before applying any other operations.

Explore the detailed steps to simplify the expression −1/2(8×14÷2+5−(6−∣−6∣)−7). This problem involves key algebraic concepts such as absolute value, order of operations (PEMDAS), and fraction multiplication. Suitable for students in Grades 7-9.

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