Question

How do you solve the inequality `3t + 1 < t + 12`?

Answer 1

`t<11/2`

Explanation:

The key realization here is that, for the most part, we can treat this like an equation. If we had

`3t+1=t+12`

we would subtract `1` from both sides, and subtract `t`. We can do the same thing with `3t+1<t+12`. We get

`3t< t+11`

`=>2t<11`

Dividing both sides by `2`, we get

`t<11/2`

Hope this helps!

Answer 2

`t<11/2`

Explanation:

`"collect terms in t on the left side and numeric values on"`
`"the right side"`

`"subtract "t" from both sides"`

`3t-t+1< cancel(t)cancel(-t)+12`

`2t+1< 12`

`"subtract 1 from both sides"`

`2t<11`

`"divide both sides by 2"`

`t<11/2" is the solution"`

`t in(-oo,11/2)larrcolor(blue)"in interval notation"`