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The problem reads:

"If \( a = -3 \), \( b = 4 \), and \( c = 10 \), what is the value of the expression below?"

\[
\frac{2(b^2 - a^2)}{c} + \frac{1}{2}
\]

### Step-by-step solution:

1. **Substitute the values of \( a \), \( b \), and \( c \):**

   - \( a = -3 \)
   - \( b = 4 \)
   - \( c = 10 \)

   So, the expression becomes:

   \[
   \frac{2(4^2 - (-3)^2)}{10} + \frac{1}{2}
   \]

2. **Calculate \( b^2 \) and \( a^2 \):**

   - \( b^2 = 4^2 = 16 \)
   - \( a^2 = (-3)^2 = 9 \)

   Now, substitute these values into the expression:

   \[
   \frac{2(16 - 9)}{10} + \frac{1}{2}
   \]

3. **Simplify inside the parentheses:**

   \[
   16 - 9 = 7
   \]

   Now, the expression becomes:

   \[
   \frac{2 \times 7}{10} + \frac{1}{2}
   \]

4. **Multiply and simplify:**

   \[
   \frac{14}{10} + \frac{1}{2}
   \]

5. **Convert the fractions to have the same denominator:**

   \[
   \frac{14}{10} + \frac{5}{10} = \frac{14 + 5}{10} = \frac{19}{10}
   \]

6. **Simplify the result:**

   \[
   \frac{19}{10} = 1.9
   \]

Thus, the value of the expression is **1.9**.

---

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. What is the value of the expression \( \frac{2(b^2 - a^2)}{c} \) if \( a = 5 \), \( b = 2 \), and \( c = 3 \)?
2. How does the value of \( a \) being negative affect the expression?
3. Can you solve a similar expression but with different constants, say \( a = 1 \), \( b = 3 \), \( c = 8 \)?
4. What happens if \( a = b \) in this type of expression?
5. How would you solve the expression if the second term was \( \frac{1}{3} \) instead of \( \frac{1}{2} \)?

**Tip:** Always simplify powers and parentheses first to make calculations easier.

If a = -3, b = 4, and c = 10, what is the value of the expression below? (2(b^2 - a^2)/c) + 1/2

Learn how to solve the expression 2(b^2 - a^2)/c + 1/2 when a = -3, b = 4, and c = 10. Follow a step-by-step solution involving algebraic concepts such as substitution and quadratic expressions. This problem is suitable for students in Grades 7-9.

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