Question

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

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(1)` and `color(blue)(t)` from each side of the inequality to isolate the `t` term while keeping the inequality balanced:

`3t - color(blue)(t) + 1 - color(red)(1) < t - color(blue)(t) + 12 - color(red)(1)`

`3t - 1color(blue)(t) + 0 < 0 + 11`

`(3 - 1)color(blue)(t) < 11`

`2t < 11`

Now, divide each side of the inequality by `color(red)(2)` to solve for `t` while keeping the inequality balanced:

`(2t)/color(red)(2) < 11/color(red)(2)`

`(color(red)(cancel(color(black)(2)))t)/cancel(color(red)(2)) < 11/2`

`t < 11/2`

Answer 2

`t<11/2` or `t<5.5`

Explanation:

act as though the '<' sign is an equals '=' sign.
put all unknowns on the same side of the equation.
`3t+1-t<12`
simplify.
`2t+1<12`
minus any numbers that do not include the unknown.
`2t<11`
isolate the unknown.
`t<11/2` or `t<5.5`