Hi, there.
______
Start off by noting that
can be either positive or negative.
First off let's solve for x, where
is a positive.
Thus,
![2x+5 < 4\\2x < -1\\x < -\dfrac{1}{2}](https://tex.z-dn.net/?f=2x%2B5%20%3C%204%5C%5C2x%20%3C%20-1%5C%5Cx%20%3C%20-%5Cdfrac%7B1%7D%7B2%7D)
Now let's solve for x, where
is a negative. But first we need to distribute -1.
.
Now solve.
![-2x-5 < 4\\-2x < 9\\x < -\dfrac{9}{2}](https://tex.z-dn.net/?f=-2x-5%20%3C%204%5C%5C-2x%20%3C%209%5C%5Cx%20%3C%20-%5Cdfrac%7B9%7D%7B2%7D)
Hope the answer - and explanation - made sense,
happy studying.
Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.
Multiply both top and bottom by that number.
Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)
<u>Answer-</u>
<em>After 7 hours number of organisms would be </em><em>19531</em>
<u>Solution-</u>
At hour one, there is one organism. At hour two, there are five more organisms.
So the number of organism in each hour would be,
1, 5, 25, 125,......... so on
This series is in Geometrical Progression.
Sum of first n terms of a G.P.
![S_n=\dfrac{a(r^n-1)}{r-1}](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Ba%28r%5En-1%29%7D%7Br-1%7D)
where,
a = first term = 1
r = common ratio = 5
n = 7
Putting the values,
![S=\dfrac{1(5^7-1)}{5-1}](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7B1%285%5E7-1%29%7D%7B5-1%7D)
![=\dfrac{5^7-1}{4}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B5%5E7-1%7D%7B4%7D)
![=\dfrac{78125-1}{4}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B78125-1%7D%7B4%7D)
![=\dfrac{78124}{4}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B78124%7D%7B4%7D)
![=19531](https://tex.z-dn.net/?f=%3D19531)
Therefore, after 7 hours number of organisms would be 19531
x = interest paid altogether
400 + 400(0.175) = x
The 400 comes from the average balance. 400(0.175) comes from the interest she has to pay each month. 1.75% as a decimal is 0.175. It's multiplied since she pays 1.75% of the average balance.