Question

always-equal outputs
here are two number machines that always give the same outputs for any input.
use the two expressions to explain why both machines will give the same outputs for any input.

Explanation:

Step1: Simplify first expression

Combine like terms:
$t + 6 + 2t = (t + 2t) + 6 = 3t + 6$

Step2: Simplify second expression

Apply distributive property:
$3(2 + t) = 3\times2 + 3\times t = 6 + 3t$

Step3: Compare simplified forms

$3t + 6 = 3t + 6$ (addition is commutative)

Answer:

When both expressions are simplified, they result in the same equivalent expression $3t + 6$. Since equivalent expressions produce identical outputs for any input value of $t$, the two number machines will always give the same outputs.