1. Exercise Write an equation or inequality for the following sentence.
Four less than a number equals seven.

2. Exercise Write an equation or inequality for the following sentence.
Four less a number equals seven.

3. Exercise Write an equation or inequality for the following sentence.
Four is less than a number plus seven.

4. Exercise Write an equation or inequality for the following sentence.
Four more than a number is greater than or equal to six.

5. Exercise Write an equation or inequality for the following sentence.
Six greater than a number is more than 4.

6. more than
less than

7. at least
at most

8. no more than
not more than

9. no less than
not less than

10. everything except

11. Example 1 Write an inequality for the following.
Five more than a number is at most sixteen.

12. Example 1 Write an inequality for the following.
Janice has three times as many nickels as Tom. Janice has fewer than 24 nickels.

13. Example 2
Elisa knows that she has at least $120 in her savings account. She wants her savings split into three categories with equal amounts in each category. What is the least amount that she has available to spend in each category?

14. Example 2
x = the amount in each category
3x ≥ 120
3x 3
120 3 ≥
x ≥ 40

15. Example 3
Mr. Haney has taken a job where he earns $2,570 per month. He tithes 10% of his income. How long will it take him to earn more than $23,000, excluding his tithe? Round your answer to the next full month.

16. Example 3 m = the number of months 2,313m > 23,000 2,313m 2,313
m > 9.9; He must work 10 months.

17. Example 4
A car buyer wants to finance a car for 24 months and keep his monthly payments less than $300. He has $1,500 available for a down payment. Will he be able to buy an $8,988 car and meet his goal?

18. Example 4 m = the monthly payment 1,500 + 24m ≥ 8,988 − 1,500 − 1,500
− 1, − 1,500 ≥
24m
7,488 24
m ≥ $312

19. Example 5
A will contains the provision that the estate, worth $64,892, be divided equally among six relatives. However, at least $12,500 is to be held in trust for a missing son for up to one year.

20. Example 5
If he is not found within that time, the money will go to the deceased's favorite charity. How much will each of the six relatives get?

21. Example 5 x = the amount per relative 64,892 − 6x ≥ 12,500
− 64, − 64,892
− 52,392
−6x ≥ − 52,392 −6
x ≤ 8,732

22. Example Write an equation or inequality and solve.
Mr. Acker wants to sell 250 watermelons and make at least $1,000. How much should he sell each of them for?
250x ≥ 1,000; at least $4

23. Example Write an equation or inequality and solve.
Mitch and Kevin have more than 475 baseball cards together. Kevin has four times as many as Mitch. How many cards does Mitch have?
x + 4x > 475; more than 95

24. Example Write an equation or inequality and solve.
Jen has 8 fewer than Mary. Together they have more than 28. How many does Mary have?
x + x − 8 > 28; more than 18

25. Example Write an equation or inequality and solve.
The three teams have over 100 points combined. The first team has three times as many as each of the other two. How many points do the second and third teams have?
3x + x + x > 100; more than 20

26. Example Write an equation or inequality and solve.
You can buy three shirts and one pair of shoes for less than $150. If the shoes cost $75, how much can you spend on each shirt?
3x + 75 < 150; at most $25

27. Example
The adult ticket was twice the cost of the child ticket. Together they cost more than $ What was the cost of the child ticket?

28. Example
The Averys have budgeted $500 for their weekend trip. If their six meals will cost an average of $28 each and gas will cost $120, what is the maximum they can spend on a hotel for each of two nights?

29. Example
Caleb is mowing grass to earn at least $340 needed for a new mountain bike. How many yards will he need to mow at $25 each to pay for the bike if he already has $60?

30. Example
Becca’s bill for school clothes was over $224. The jacket cost three times as much as the skirt. The three shirts were $21 each. Find the cost of the skirt and jacket.

31. Example
If Jake puts $150 in his savings account and adds $75 each week, how many weeks will it take him to save over $1,000?