# solving and graphing system of inequalities

1. determine whether the given numbers are solutions of the inequality. 7, -13, -17, -1

y-10>2y-4 is 7 a solution?

2. write the set (xlx_>1) in interval notation

3. write interval notation for the set (xl-1>x>-3)

4. write interval notation for the given graph ( straight line graph shaded from -7 to 9

5. solve then graph. T+16_>5

6. solve: -7/2x_>-5/4

7. 6x+1<43

8. 0.6x+2<_1.0x-1

9. solve. 2/3(3x-6)>12

10. The body mass index, I, can be used to determine an individual's risk for heart disease. An index less than 25 indicates a low risk. The body mass index is gven by the formula, or model, I=700W/H^2, where W=weight, in pounds, and H=height, in inchese. Francis weighs 166 plbs and stand 75 inches tall. What is his approximate body mass index? Find an inequality describing all weights W that Francis can have and be in the low risk category.

11 .Bayside insurance offers two health plans. Under plan A, Giselle would have to pay the first $60 fo her medical bills, plus 25% of the rest. Under plan B, Gisells would pay the first $90 but only 20% of the rest. For what amount of the medical bills will plan B save Giselle Money? Assume she has over $90 in bills

12. Find the intersection (2,5,7,10)-(3,6,8)

13.graph and write the solution in interval notation x<9 and x_>-6

14.solve and graph -9<_3x+3 and 3x+3<12

15.solve -4<x+4<8

16. solve -22<_4x-9<_-4

17. graph the compound inequality. Write the solution using interval notation

x<-1 or x>0

18. solve and graph: x+5<-3 or x+5>3

19. solve: 2x-1/10<_-7 or 2x-1/10_>5

20.in order to achieve maximum results from aerobic exercise, one should maintain one's heart rate at a certain level. A 45 yr old woman with a resting heart rate of 70 beats per minute should keep her heart rate between 133 and 154 beats per minute while exercising. She checks her pulse for 10 sec while exercising. What shoul the number of beats be?

The number of beats in 10 sec should be between _ and _ beats

21.determine whether the ordered pais is a solution of the inequality: (-3,7);9x+7<-7

22. graph the inequality on a plane: y>4x

23. graph the inequality on a plane: 4x+5y<_20

24. graph the inequality on a plane: 5x-4<_9x+y

25. match each graph with the appropriate inequality

26. match each graph with the appropriate inequality

27. graph the system of inequalities: y>_ -4, x>_ 6

28. graph the system of inequalities: x+2y<_4, 2x+y<_4, x_>0, y_>0

#### Solution Summary

The solution is comprised of step-by-step explanations of solving and solving and graphing system of inequalities. It also shows how to write the inequality in interval notation.