Evaluate 3(x – 4) + 2x – x2 for x = 5.

To evaluate the expression \( 3(x - 4) + 2x - x^2 \) for \( x = 5 \), follow these steps:

1. **Substitute \( x = 5 \) into the expression:**

   \[
   3(5 - 4) + 2(5) - 5^2
   \]

2. **Simplify inside the parentheses:**

   \[
   3(1) + 2(5) - 5^2
   \]

3. **Multiply and square the values:**

   \[
   3 \times 1 + 2 \times 5 - 25
   \]

   \[
   3 + 10 - 25
   \]

4. **Add and subtract the results:**

   \[
   13 - 25 = -12
   \]

So, the value of the expression when \( x = 5 \) is \( \boxed{-12} \).

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

Here are five related questions to expand your understanding:

1. What happens if you evaluate the same expression for \( x = -5 \)?
2. How would the expression change if the \( x^2 \) term had a positive coefficient?
3. What is the significance of the order of operations in this expression?
4. How does the value of the expression change as \( x \) increases or decreases?
5. Can you factor the expression before substituting the value of \( x \)?

**Tip:** Always perform operations inside parentheses first before moving on to multiplication, division, addition, and subtraction.

Learn how to evaluate the expression 3(x – 4) + 2x – x^2 for x = 5 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and quadratic equations. Suitable for students in Grades 7-9.

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