could someone help me revise these Inequalities problems? my answers are under the question...

Question

For questions, #3 #4 and #5 my teacher said "equals as well?"
For question #8 my teacher said "where's the inequality sign?"

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?

The cost of Joe’s car is x. So it is greater than $8500 but less than $12000.

$8500<x<12000

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?

The number of hours that Sarah is x. Which is 2 hours less than the typical hours of sleep, 8,

8-2=6

6<x<8



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.

Women’s requirements are x. They need 600 fewer calories than the minimum of a man’s requirements which are between 2200 and 2800.

1600<x<2200

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

Interest rate is 3% per year, put 3% in decimal form ~ 3/100=0.03
5000*0.03*10=$1500
The answer is ~ interest rate needed to earn at least $1500 of interest is 3%

Answer 1

at least means >= (not less)
at most means <= (not more)

#3: 8500 <= x <= 12000
#4 between usually includes the end points. So 6 <= x <= 8
#5: same idea

#8: Using simple interest,
5000(1+10r) >= 1500
1+10r >= 1.30
10r >= 0.3
r >= 0.03
so, at least 3%

Answer 2

Thank you so much!!