Question

What is the value of this expression when r = -2?

2r2 + |r + 7| - 5

12

4

8

-8

Answer 1

To evaluate the expression \( 2r^2 + |r + 7| - 5 \) when \( r = -2 \), we'll substitute \(-2\) for \(r\) and simplify step by step.

1. Substitute \( r = -2 \):
\[
2(-2)^2 + |-2 + 7| - 5
\]

2. Calculate \( (-2)^2 \):
\[
(-2)^2 = 4
\]

3. Substitute back into the expression:
\[
2(4) + |-2 + 7| - 5
\]

4. Multiply:
\[
8 + |-2 + 7| - 5
\]

5. Simplify inside the absolute value:
\[
-2 + 7 = 5
\]

6. Now the expression is:
\[
8 + |5| - 5
\]

7. Since the absolute value of 5 is 5, we have:
\[
8 + 5 - 5
\]

8. Now simplify:
\[
8 + 5 = 13
\]
\[
13 - 5 = 8
\]

Thus, the value of the expression when \( r = -2 \) is \( \boxed{8} \).