Question

Collin is substituting t = 2 and t = 6 to determine if the two expressions are equivalent.

3 (t + 5) 3 t + 5

Which statement is true?
Both expressions are equivalent to 11 when t = 2.
Both expressions are equivalent to 33 when t = 6.
Both expressions are equivalent to 23 when t = 6.
The expressions are not equivalent.

Answer 1

Let's evaluate both expressions \(3(t + 5)\) and \(3t + 5\) for \(t = 2\) and \(t = 6\) to determine if they are equivalent.

**When \(t = 2\):**

1. For the first expression:
\[
3(t + 5) = 3(2 + 5) = 3(7) = 21
\]

2. For the second expression:
\[
3t + 5 = 3(2) + 5 = 6 + 5 = 11
\]

So, when \(t = 2\), the values are:
- \(3(t + 5) = 21\)
- \(3t + 5 = 11\)

They are **not equivalent** when \(t = 2\).

---

**When \(t = 6\):**

1. For the first expression:
\[
3(t + 5) = 3(6 + 5) = 3(11) = 33
\]

2. For the second expression:
\[
3t + 5 = 3(6) + 5 = 18 + 5 = 23
\]

So, when \(t = 6\), the values are:
- \(3(t + 5) = 33\)
- \(3t + 5 = 23\)

They are **not equivalent** when \(t = 6\) either.

---

### Conclusion:
Based on the calculations, the correct statement is:
**The expressions are not equivalent.**