Question

explain whether 14t - 3t is equivalent to 3t - 14t. support your answer by evaluating the expressions for t = 2.

the expression 14t - 3t dropdown equivalent to 3t - 14t because the negative sign in 14t - 3t belongs to the term blank.

Explanation:

Step1: Evaluate \( 14t - 3t \) when \( t = 2 \)

First, simplify \( 14t - 3t \) to \( (14 - 3)t = 11t \). Then substitute \( t = 2 \): \( 11\times2 = 22 \).

Step2: Evaluate \( 3t - 14t \) when \( t = 2 \)

Simplify \( 3t - 14t \) to \( (3 - 14)t = - 11t \). Substitute \( t = 2 \): \( - 11\times2 = - 22 \).

Step3: Analyze the signs

In \( 14t - 3t \), the negative sign is associated with the term \( 3t \) (since it's \( 14t + (- 3t) \)). The two expressions simplify to \( 11t \) and \( - 11t \) respectively, which are not equal (except when \( t = 0 \), but for \( t = 2 \) they differ). So \( 14t - 3t \) is not equivalent to \( 3t - 14t \).

Answer:

The expression \( 14t - 3t \) is not equivalent to \( 3t - 14t \) because the negative sign in \( 14t - 3t \) belongs to the term \( 3t \). (When \( t = 2 \), \( 14t - 3t=22 \) and \( 3t - 14t = - 22 \), so they are not equal.)