Question

the number t is rational. which statement about t + 2 is true?
t + 2 is rational.
t + 2 is irrational.
t + 2 can be rational or irrational, depending on the value of t.

Explanation:

Step1: Recall rational number definition

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$. If $t$ is rational, then $t = \frac{a}{b}$ for some integers $a,b$ ($b
eq0$).

Step2: Analyze $t + 2$

We can write $t + 2$ as $\frac{a}{b}+2=\frac{a + 2b}{b}$. Here, $a + 2b$ is an integer (since $a$ and $b$ are integers), and $b
eq0$. So $t + 2$ can be expressed as a fraction of two integers with a non - zero denominator, which means $t + 2$ is rational.

Answer:

$t + 2$ is rational.