Expert: Richard J. Raridon - 7/15/2010

Question
1. Solve the inequality:

  2r + 5 < -1

2. Solve the inequality:

  3/4 k < -6

3. Solve the inequality:

  3t ≥ 6t + 12

4. Solve the inequality:

  1 + 2x < 2(x-1)

5. Solve the inequality:

  3(x-2) - 2 < x - 5

6. Solve the inequality:

  4s + 3(2-3s) ≤ 5(2-s)

7. Solve the inequality:

  4(2-x) - 3(1+x) < 5(1-x)

8. Solve:

  2/3t-( 2 - 3 t ) < 5t + 2 ( 1 - t )

9. Solve:

  4[5x - (3x-7)] ≤ 2(4x-5)

10. 5^2 - 7^2/ 5 - 7

11.  -2 (5 - 8)3

12. Simplify:

   4(3-m) - (2m+1)

13. Solve:

   2 > y + 2 ≥ 0

14. Solve:

   -1 ≤ 3z + 2 ≤ 8

15. Solve:

   3k + 7 < 1 or 2k - 3 >1

16. Solve:

   2x + 3 > 1 or 5x - 9 ≤ 6

17. The usual toll charge to use the Bingham tunnel is 50 cents.  If you purchase a special sticker for $5.50, the toll is only 35 cents.  At least how many trips through the tunnel are needed before the sticker costs less than paying for each trip separately?

18. The lengths of the legs of an isosceles triangle are integers.  The base is half as long as each leg.  What are the possible lengths of the legs if the perimeter is between 6 units and 16 units?

19. Find three consecutive multiples of 15 such that twice their sum is 360.

20. The second of three numbers is 4 times the first number.  The third number is 12 less than the first.  Find the three numbers given that their sum is 42.

21. There are three consecutive even integers such that the sum of the second and third integers is 30 more than the first integer.  Find these three even integers.

22. Find all sets of three consecutive even integers whose sum is between 25 and 45.

23. Jim's second test score was 8 points higher than his first test score.  His third score was 88.  He had a B average (between 80 and 89, inclusive) for the three tests.  What can you conclude about his first test score?  It was between:

24. The three sides of an equilateral triangle are increased by 20 cm, 30 cm, and 40 cm, respectively.  The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle.  What can you conclude about the length of a side of the original triangle?  It is between:

25. During the first 20 miles of a 50 mile bicycle race, Roger's average speed was 16 mi/h.  What must his average speed be during the remainder of the race if he is to finish the race in less than 2.5 hours?  Greater than:

26. The length of a rectangular sheet of paper was twice its width.  After 1 cm was trimmed from all four edges of the sheet, the perimeter was at most 1 m.  Find the largest possible dimensions of the trimmed sheet.

27. 1/2t ≤ -2 or t - 4 ≥  -3

28. Solve:

   -2y < -6 or y + 3 ≤ 1

29. Solve:

   -1 < 5 - 2p < 5

30. Solve:

   2x + 3 > 1 and 5x - 9 ≤ 6

31. -6 ≤ 2 - 3m ≤ 7

32.  ≥  1 - n/2> -2

33. Solve:

  5n - 1 > 0 and 4n + 2 < 0

34. Solve:

   3y + 5 ≥ 2y + 1 > y - 1

35. Solve:

   3z + 7 ≤ 4z or 3z + 7 < -4z

36. Solve:

   -5 < 2(2-s) + 1 ≤ 9

37. solve:

   y-3/6 y - 1 or  y-6/3 ≥ y + 4

Answer
1- r<-3
2- k<-8
3- t>=-4
4- no solution
5- x<3/2
6- no solution
7- x<0
8- t<6
9- no solution
10- 12
11- 18
12- 11-6m
13- -2<=y<0
14- -1<=z<=2
15- k<-2 or k>2
16- x<=3
17- 16
18- 2,4,4 or 3,6,6
19- not possible
20- 9,36,-3
21- 24,26,28
22- 8,10,12 or 10,12,14 or 12,14,16
23- 72<x<85
24- 15-30
25- 24mph
26- 16x34
27- t<=-4 or t>1
28- y<3 or y<=-2
29- 0<p<3
30- x>-1 or x<=3
31- -1<m<=2
32- ?
33- n<-1/2 or n>1/5
34- ?
35- z<=-7 or z>=1
36- -2<=s<5
37- ?
Ordinarily, I don't work this many problems for one person since I have many who only send me a few problems.