Question

Cadence is substituting t = 4 and t = 6 to determine if the two expressions are equivalent.

2 (7 t minus 3) 15 t minus 12

Which statement is true?
Both expressions are equivalent to 78 when t = 6.
Both expressions are equivalent to 81 when t = 6.
Both expressions are equivalent to 48 when t = 4.
The expressions are equivalent.

Answer 1

Let's calculate each expression for \( t = 4 \) and \( t = 6 \) to determine if they are equivalent.

1. **For \( t = 4 \)**:
- First Expression: \( 2(7t - 3) \)
\[
2(7(4) - 3) = 2(28 - 3) = 2(25) = 50
\]
- Second Expression: \( 15t - 12 \)
\[
15(4) - 12 = 60 - 12 = 48
\]

For \( t = 4 \):
- The first expression equals **50**, and the second expression equals **48**.

2. **For \( t = 6 \)**:
- First Expression: \( 2(7t - 3) \)
\[
2(7(6) - 3) = 2(42 - 3) = 2(39) = 78
\]
- Second Expression: \( 15t - 12 \)
\[
15(6) - 12 = 90 - 12 = 78
\]

For \( t = 6 \):
- Both expressions equal **78**.

### Conclusion
- When \( t = 4 \): **50** (First) vs **48** (Second) - **not equivalent**.
- When \( t = 6 \): **78** (Both) - **equivalent**.

The true statement is:
**Both expressions are equivalent to 78 when t = 6.**