Answer:
![\large\boxed{x](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%3C12%5Cto%20x%5Cin%28-%5Cinfty%2C%5C%2012%29%7D)
Step-by-step explanation:
![6-2x>-18\qquad\text{subtract 6 from both sides}\\\\6-6-2x>-18-6\\\\-2x>-24\qquad\text{change the signs}\\\\2x](https://tex.z-dn.net/?f=6-2x%3E-18%5Cqquad%5Ctext%7Bsubtract%206%20from%20both%20sides%7D%5C%5C%5C%5C6-6-2x%3E-18-6%5C%5C%5C%5C-2x%3E-24%5Cqquad%5Ctext%7Bchange%20the%20signs%7D%5C%5C%5C%5C2x%3C24%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5C%5C%5Cdfrac%7B2x%7D%7B2%7D%3C%5Cdfrac%7B24%7D%7B2%7D%5C%5C%5C%5Cx%3C12)
Answer:
The interest rate was of 5.5% a year.
Step-by-step explanation:
The compound interest formula is given by:
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.
In this question, we have that:
![A = 109076.45, P = 98000, n = 1, t = 2](https://tex.z-dn.net/?f=A%20%3D%20109076.45%2C%20P%20%3D%2098000%2C%20n%20%3D%201%2C%20t%20%3D%202)
We have to find r.
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![109076.45 = 98000(1 + r)^{2}](https://tex.z-dn.net/?f=109076.45%20%3D%2098000%281%20%2B%20r%29%5E%7B2%7D)
![(1+r)^{2} = \frac{109076.45}{98000}](https://tex.z-dn.net/?f=%281%2Br%29%5E%7B2%7D%20%3D%20%5Cfrac%7B109076.45%7D%7B98000%7D)
![(1+r)^{2} = 1.113025](https://tex.z-dn.net/?f=%281%2Br%29%5E%7B2%7D%20%3D%201.113025)
Taking the square root from both sides to isolate r.
![\sqrt{(1+r)^{2}} = \sqrt{1.113025}](https://tex.z-dn.net/?f=%5Csqrt%7B%281%2Br%29%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B1.113025%7D)
![1 + r = 1.055](https://tex.z-dn.net/?f=1%20%2B%20r%20%3D%201.055)
![r = 1.055 - 1](https://tex.z-dn.net/?f=r%20%3D%201.055%20-%201)
![r = 0.055](https://tex.z-dn.net/?f=r%20%3D%200.055)
The interest rate was of 5.5% a year.
Hey there!
Ratios can also be expressed as fractions. The first number will be your numerator while the second number will be your denominator.
![7:3 = \frac{7}{3} =2 \frac{1}{3}](https://tex.z-dn.net/?f=7%3A3%20%3D%20%20%5Cfrac%7B7%7D%7B3%7D%20%3D2%20%5Cfrac%7B1%7D%7B3%7D%20)
![8:4 = \frac{8}{4} = 2](https://tex.z-dn.net/?f=8%3A4%20%3D%20%20%5Cfrac%7B8%7D%7B4%7D%20%3D%202)
![9:5 = \frac{9}{5} = 1 \frac{4}{5}](https://tex.z-dn.net/?f=9%3A5%20%3D%20%20%5Cfrac%7B9%7D%7B5%7D%20%3D%201%20%5Cfrac%7B4%7D%7B5%7D%20)
![2:7 = \frac{2}{7}](https://tex.z-dn.net/?f=2%3A7%20%3D%20%5Cfrac%7B2%7D%7B7%7D%20)
You could then divide these fractions out by dividing the numerator by the denominator to see which is the largest, but we can already tell that 2 1/3, or 7:3, will be the largest, since none of the other fractions are that large.
Hope this helped you out! :-)
X=6 because 3X6=18 so x=6