Answer:
x > 15
Step-by-step explanation:
simplify both sides of the inequality
2x + 9 > 39
subtract 9 from both sides
2x + 9 - 9 > 39 -9
2x > 30
divide both sides by 2
2x/2 > 30/2
x > 15
They need to make sure you will be able to pay the loan back
Hope this helps :)
Step-by-step explanation:
1 x 12 = 12
2 x 6 = 12
3 x 4 = 12
1, 2, 3, 4, 6, 12
![{ \qquad\qquad\huge\underline{{\sf Answer}}}](https://tex.z-dn.net/?f=%7B%20%5Cqquad%5Cqquad%5Chuge%5Cunderline%7B%7B%5Csf%20Answer%7D%7D%7D%20)
Here we go ~
Let's calculate its discriminant :
![\qquad \sf \dashrightarrow \: 4 {u}^{2} + 16u + 41 = 40](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%204%20%7Bu%7D%5E%7B2%7D%20%20%2B%2016u%20%2B%2041%20%3D%2040)
![\qquad \sf \dashrightarrow \: 4 {u}^{2} + 16u + 41 - 40 = 0](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%204%20%7Bu%7D%5E%7B2%7D%20%20%2B%2016u%20%2B%2041%20-%2040%20%3D%200)
![\qquad \sf \dashrightarrow \: 4 {u}^{2} + 16u + 1 = 0](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%204%20%7Bu%7D%5E%7B2%7D%20%20%2B%2016u%20%2B%201%20%20%3D%200)
Here, if we equate it with general equation,
![\qquad \sf \dashrightarrow \: disciminant = {b}^{2} - 4ac](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20disciminant%20%3D%20%20%7Bb%7D%5E%7B2%7D%20%20-%204ac)
![\qquad \sf \dashrightarrow \: d = (16) {}^{2} - (4 \times 4 \times 1)](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20d%20%3D%20%2816%29%20%7B%7D%5E%7B2%7D%20-%20%284%20%5Ctimes%204%20%5Ctimes%201%29%20)
![\qquad \sf \dashrightarrow \: d = (16) {}^{2} - (16)](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20d%20%3D%20%2816%29%20%7B%7D%5E%7B2%7D%20-%20%2816%29%20)
![\qquad \sf \dashrightarrow \: d = 16(16 - 1)](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20d%20%3D%2016%2816%20-%201%29)
![\qquad \sf \dashrightarrow \: d = 16(15)](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20d%20%3D%2016%2815%29)
![\qquad \sf \dashrightarrow \: d = 240](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20d%20%3D%20240)
Now, since discriminant is positive ; it has two real roots ~
The roots are :
![\qquad \sf \dashrightarrow \: u = \dfrac{ - b \pm \sqrt{ d } }{2a}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20u%20%3D%20%20%5Cdfrac%7B%20-%20b%20%5Cpm%20%5Csqrt%7B%20d%20%7D%20%7D%7B2a%7D%20)
![\qquad \sf \dashrightarrow \: u = \dfrac{ - 16\pm \sqrt{ 240 } }{2 \times 4}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20u%20%3D%20%20%5Cdfrac%7B%20-%2016%5Cpm%20%5Csqrt%7B%20240%20%7D%20%7D%7B2%20%5Ctimes%204%7D%20)
![\qquad \sf \dashrightarrow \: u = \dfrac{ - 16\pm 4\sqrt{ 15 } }{8}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20u%20%3D%20%20%5Cdfrac%7B%20-%2016%5Cpm%204%5Csqrt%7B%2015%20%7D%20%7D%7B8%7D%20)
![\qquad \sf \dashrightarrow \: u = \dfrac{ 4(- 4\pm \sqrt{ 15 }) }{8}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20u%20%3D%20%20%5Cdfrac%7B%204%28-%204%5Cpm%20%5Csqrt%7B%2015%20%7D%29%20%7D%7B8%7D%20)
![\qquad \sf \dashrightarrow \: u = \dfrac{ - 4\pm \sqrt{ 15 } }{2}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20u%20%3D%20%20%5Cdfrac%7B%20-%204%5Cpm%20%5Csqrt%7B%2015%20%7D%20%7D%7B2%7D%20)
So, the required roots are :
![\qquad \sf \dashrightarrow \: u = \dfrac{ - 4 - \sqrt{ 15 } }{2} \: \: and \: \: \dfrac{ - 4 + \sqrt{15} }{2}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20u%20%3D%20%20%5Cdfrac%7B%20-%204%20-%20%20%5Csqrt%7B%2015%20%7D%20%7D%7B2%7D%20%20%5C%3A%20%20%5C%3A%20and%20%5C%3A%20%20%5C%3A%20%20%5Cdfrac%7B%20-%204%20%2B%20%20%5Csqrt%7B15%7D%20%7D%7B2%7D%20)