Could someone please show me how to do these problems? 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~~

Question

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.

1. Carlos spends at least 45 minutes each day on the Internet. Which inequality could be used to describe the amount of time, x, that Carlos spends on the Internet?


2. Amrita spends at most 2 hours watching television each night. Which inequality could be used to describe the amount of time, x, that Amrita spends watching television each night?


3. Joe expects to spend at least $8500 on a used car, but he can’t afford to spend more than $12,000. Which inequality could be used to describe the amount of money, x, that Joe may spend on a car?


4. Teenagers should sleep between 8 and 10 hours per night. Sarah typically sleeps 2 hours less than this per night. Which inequality describes the amount of time that Sarah sleeps?


5. Men need to intake between 2200 and 2800 calories daily. Women need 600 fewer calories than this. Write and solve an inequality to discover how many calories women should be taking in per day.

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

3(x-2) + 4 > 2(2x-3).
3x-6 + 4 > 4x-6.
3x-4x > -6 + 2.
-x > -4.
X < 4.

1. X => 45 min.

2. X =< 2 hrs.

3. $8500 =< X < $12,000.