Question -
Answer -
Given:
| (3x тАУ 4)/2 | тЙд 5/12
We can rewrite it as
| 3x/2 тАУ 4/2 | тЙд 5/12
| 3x/2 тАУ 2 | тЙд 5/12
Let тАШrтАЩ be a positive real number and тАШaтАЩ be a fixed real number. Then,
|x тАУ a| тЙд r тЯ║ a тАУ r тЙд x тЙд a + r
Here, a = 2 and r = 5/12
2 тАУ 5/12 тЙд 3x/2 тЙд 2 + 5/12
(24-5)/12 тЙд 3x/2 тЙд (24+5)/12
19/12 тЙд 3x/2 тЙд 29/12
Now, multiplying the whole inequality by 2 and dividing by 3, we get
19/18 тЙд x тЙд 29/18
тИ┤ x тИИ [19/18, 29/18]