<h3>All options satisfies the given inequality</h3>
<em><u>Solution:</u></em>
Given that,
![y < | 3x | + 1](https://tex.z-dn.net/?f=y%20%3C%20%7C%203x%20%7C%20%2B%201)
Here, modulus means that, the absolute value of a number is never negative
<em><u>Option A</u></em>
![(2, -9)](https://tex.z-dn.net/?f=%282%2C%20-9%29)
Substitute x = 2 and y = -9 in given
![-9 < | 3(2)| + 1\\\\-9 < 6 + 1\\\\-9 < 7](https://tex.z-dn.net/?f=-9%20%3C%20%7C%203%282%29%7C%20%2B%201%5C%5C%5C%5C-9%20%3C%206%20%2B%201%5C%5C%5C%5C-9%20%3C%207)
-9 is less than 7 is true
This forms a solution to given inequality
<em><u>Option B</u></em>
(-4, 12)
Substitute x = -4 and y = 12 in given
![12 < | 3(12)| + 1\\\\12 < 36 + 1\\\\\12 < 37](https://tex.z-dn.net/?f=12%20%3C%20%7C%203%2812%29%7C%20%2B%201%5C%5C%5C%5C12%20%3C%2036%20%2B%201%5C%5C%5C%5C%5C12%20%3C%2037)
12 is less than 37 is true
This forms a solution to given inequality
<em><u>Option C</u></em>
(3, 15)
Substitute x = 3 and y = 15 in given
![15 < | 3(15)| + 1\\\\15 < 45+1\\\\15< 46](https://tex.z-dn.net/?f=15%20%3C%20%7C%203%2815%29%7C%20%2B%201%5C%5C%5C%5C15%20%3C%2045%2B1%5C%5C%5C%5C15%3C%2046)
15 less than 46 is true
This forms a solution to given inequality
<em><u>Option D</u></em>
(0, 0)
Substitute x = 0 and y = 0 in given
![0 < | 3(0) | + 1\\\\0 < 0 + 1\\\\0 < 1](https://tex.z-dn.net/?f=0%20%3C%20%7C%203%280%29%20%7C%20%2B%201%5C%5C%5C%5C0%20%3C%200%20%2B%201%5C%5C%5C%5C0%20%3C%201)
0 is less than 1
This forms a solution to given inequality