How do you solve |3h - 3| < 12|3h3|<12?

2 Answers
May 31, 2018

-3\lth\lt53<h<5

Explanation:

|x|\lta|x|<a means -a\ltx\ltaa<x<a.

\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

May 31, 2018

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 :)