Question

How do you solve `|3h - 3| < 12`?

Answer 1

`-3\lth\lt5`

Explanation:

`|x|\lta` means `-a\ltx\lta`.

`\therefore|3h-3|\lt12` means `-12\lt3h-3\lt12`
Let's isolate the term with variable (`3h`).

`-12\color(red)(+3)\lt3h-3\color(red)(+3)\lt12\color(red)(+3)`
`-9\lt3h\lt15`

Now we will isolate the variable (`h`).
`-9\color(blue)(\div3)\lt3h\color(blue)(\div3)\lt15\color(blue)(\div3)`

And so your answer is...
`-3\lth\lt5`

Answer 2

`h in (-3,5)`

Explanation:

We have,

`|3x-3|<12`
`=> 3|x-1|<12`
`=> |x-1|<4`

Now, consider the case `|x-a| < b`

Think this expression as ”X such that, its distance from a is less than b”

You can take help of the number line also to apply this statement.

So as per the question, it should be ”x such that its distance from 1 should be less than 4”

If you take the help of the number line, you will find that there will be two critical points `-3` and `5`
Since distance is less than 4, condition on x will be :-

`-3< x < 5`

Hence the answer.

Hope it helps :)