Question

Could someone please show me how to do these problems? or just show me how to do 1 or 2? I would really appreciate any help you could give... There are examples in my lesson but I don't understand them, here are the examples~~
EXAMPLE~
Solve 3(x – 2) + 4 > 2(2x – 3).
First I'll multiply through and simplify; then I'll solve:

3(x – 2) + 4 > 2(2x – 3)
3x – 6 + 4 > 4x – 6
3x – 2 > 4x – 6
–2 > x – 6 (*)
4 > x
x < 4

EXAMPLE~
The velocity of an object fired directly upward is given by V = 80 – 32t, where t is in seconds. When will the velocity be between 32 and 64 feet per second?
32 < 80 – 32t < 64
32 – 80 < 80 – 80 – 32t < 64 – 80
–48 < –32t < –16
–48 / –32 > –32t / –32 > –16 / –32
1.5 > t > 0.5

0.5 < t < 1.5

The velocity will be between 32 and 64 feet per second between 0.5 seconds after launch and 1.5 seconds after launch.

Questions~~
6. The velocity of an object fired directly upward is given by V = 20 – 9.8t, where t is time in seconds. When will the velocity be between 10 and 20 meters per second?


7. If you invest $2000 at a rate of 8% per year, how many years will it take to earn at least $1000 in interest?


8. If you invest $5000 for 10 years, which inequality describes the interest rate needed to earn at least $1500 of interest?


9. The velocity of an object fired directly upward is given by V = 35 – 9.8t, where t is time in seconds. Which inequality describes the velocity when t is between 0.5 and 1.5 seconds? (HINT: Remember that when you multiply an inequality by a negative number, you must switch the direction of the inequality.)


10. What is the least amount of principal you can invest at an 8% interest rate to earn at least $1000 in interest in 3 years? (Round your answer to the nearest dollar.)

Answer 1

The two examples you have are pretty straight-forward.
You will just have to practise and practise until you can do those.

I will do #6

10 < (20-9.8t) < 20
subtract 20 from each part
-10 < -9.8t < 0
divide each part by -9.8, remember to reverse the inequality sign
10/9.8 > t > 0
or
0 < t < appr 1.02

you can always test them by picking numbers in that domain, and then choosing some numbers outside the domain to see what the velocity is

#9 is done the same way

#7and 8 are the same type.
they both use the compound interest formula
amount = present value(1+i)^n, where i the periodic intersest rate and n is the number of interest periods
I will do #7, you try #8

7. 2000(1 + .08)^n > 3000
divide by +2000, inequality sign stays the same
1.08^n > 1.5
take logs of both sides,
log(1.08^n) > log 1.5
n log 1.08 > log 1.5
divide both sides by log1.08, which is a positive number
n > log 1.5/log 1.08
n > 5.27
So it will take about 5 1/4 years to earn at least $1000 interest (or the amount is $3000)