Question

Emily is substituting t = 8 and t = 10 to determine if the two expressions are equivalent.

6 (t minus 4) 6 t minus 24

Which statement is true?
Both expressions are equivalent to 24 when t = 8.
Both expressions are equivalent to 44 when t = 8.
Both expressions are equivalent to 46 when t = 10.
The expressions are not equivalent.

Answer 1

To determine if the two expressions \(6(t - 4)\) and \(6t - 24\) are equivalent and to evaluate them for \(t = 8\) and \(t = 10\), we will calculate each expression for both values of \(t\).

1. **For \(t = 8\)**:

- Evaluate \(6(t - 4)\):
\[
6(8 - 4) = 6(4) = 24
\]

- Evaluate \(6t - 24\):
\[
6(8) - 24 = 48 - 24 = 24
\]

Both expressions equal 24 when \(t = 8\).

2. **For \(t = 10\)**:

- Evaluate \(6(t - 4)\):
\[
6(10 - 4) = 6(6) = 36
\]

- Evaluate \(6t - 24\):
\[
6(10) - 24 = 60 - 24 = 36
\]

Both expressions equal 36 when \(t = 10\).

Given this evaluation, we can conclude that:
- Both expressions are equivalent to 24 when \(t = 8\).
- Both expressions are equivalent to 36 when \(t = 10\).

Thus, the correct statement is:
**Both expressions are equivalent to 24 when \(t = 8\)**.