Inequality

First we make the inequality clearer, this is what it looks like:

${t\over3} - 5 < t - 2$

Step 1 is to make it neater, so we multiply both sides of the inequality by 3.

$t - 15 < 3t - 6$

Then we isolate the variable by adding 6 to both sides of the inequality, then subtracting $t$ from both sides of the inequality.

$t - 9 <3t$

$-9<2t$

The last step is to divide both sides by 2 to get the interval for $t$.

-4.5 < t

4.5 can be written as 9/2, but there you have it, the interval for t!