whats the absolute time interval?

Question

For the time interval $1< \lvert t+1 \rvert \leq 3 $ I am trying to solve for t to get my range to plot a function.

I know $\lvert t+1 \rvert \leq 3 \iff -3\leq t+1 \leq 3 \iff -4 \leq t \leq 2$

And then $ \lvert t+1 \rvert > 1 $ becomes $t+1 >1 $ or $t+1 <-1$. Hence $t>0$ or $t<-2$.

Then things seem to contradict and i can't figure out my time range. What am I doing wrong?

score 1 · Accepted Answer · answered Jan 17 '13 at 07:53

1

Your work is fine. You then need to find the $t$-values that satisfy both conditions: $-4 \leq t \leq 2$ and $t \in (-\infty, -2) \cup (0, \infty)$.

Alternatively, you could consider two cases: $t + 1 \geq 0$ and $t + 1 < 0$. When $t + 1 \geq 0$, we have that $|t + 1| = t + 1$, and thus $1 < t + 1 \leq 3$ so that $0 < t \leq 2$. All of these values are permissible as we are assuming $t > -1$ in this range as $t + 1 > 0$. You could deal with the other case $t + 1 < 0$ by noting that $|t + 1| = - (t + 1)$ in this range.

answered Jan 17 '13 at 07:53

JavaMan

13,153

so i can have two different sets of intervals that can satisfy the t values? – user1945925 Jan 17 '13 at 08:21
@user1945925: I'm not sure precisely what you mean. However, you can have two different intervals which satisfy the system of inequalities. – JavaMan Jan 17 '13 at 09:13
Nice approach. +1 – Mikasa Jan 21 '13 at 08:47

whats the absolute time interval?

1 Answers1