What will be the answer of the expression $| t-2 |$?

Question

What will be the answer of the expression $| t-2 |$?

Either $t + 2$ or $t - 2$ and How ?

Answer 1

For any $x\in\mathbb{R}$, $|x|=x$ is $x\geq 0$ and $|x|=-x$ if $x<0$.

Thus, $|t-2|=t-2$ is $t-2\geq0\iff t\geq 2$ and $|t-2|=-t+2$ if $t-2<0\iff t < 2$.

Answer 2

If $t\ge 2$, we have $|t-2|=t-2$.

If $t<2$ , we have $|t-2|=-t+2=2-t$