Algebra 1 Common Core Student Edition, Grade 8-9

Write each inequality in interval notation. Then graph the interval.

27. x>-2 28. x<0 29. x<-2orx>l 30.-3<x<4

Solve each inequality. Write each set in interval notation.

31.7<x +6< 12 32. -9<3m + 6< 18

33. /+ 14 < 9 or -9 /< -45 34. 12h - 3 > 15h or 5 > -0 .2h + 1 0

Write a compound inequality that each graph could represent.

35. H 1— ® h 36. -®— I-----h
    -3 -2 -1
    37. -0 -b -®-
    -2 0

Solve each compound inequality. Justify each step.

38. 4r-3> 11 or4r-3<-11 39.2
    4y + 2


39. 5 > 3 or —4 - 3v > 4 41.

2= 0.75v — 4.5

4 _ 1 3

3-7 W- < 1

Ch em i st r y The acidity of th e w ater in a sw im m ing pool is considered n orm al if the

average of th ree pH readings is b etw e en 7.2 a n d 7.8, inclusive. The first two

readings for a sw im m ing pool are 7.4 a n d 7.9. W hat possible values for th e third

reading p will m ake th e average pH norm al?

43. Think About a Plan The Triangle Inequality Theorem states th a t th e sum
    of th e lengths of any two sides of a triangle is greater th a n th e length of
    th e third side. The lengths of two sides of a triangle are given. W hat are
    th e possible lengths x of the third side of th e triangle?
    
    
    • Is th ere an u p p e r lim it on th e value of x? Is there a low er limit?
    
    
    • How can you use your answ ers to the previous question to w rite one or
      m ore inequalities involving x?
    
    
    
    

Use your answers to Exercise 43 to answer Exercises 44-47. The lengths of two
sides of a triangle are given. Find the possible lengths of the third side.

44. 3.75 in., 7 in. 45. 15 ft, 21ft 46. 14 m m , 35 m m 47. 6 m, 17 m


45. Physics The force exerted on a spring is pro p o rtio n al to th e distance th e spring
    is stretched from its relaxed position. Suppose you stretch a spring a distance of
    d inches by applying a force of F pounds. For your spring, f = 0.8. You apply forces
    betw een 25 lb a n d 40 lb, inclusive. W hat inequality describes th e distances the
    spring is stretched?


46. Reasoning D escribe th e solutions of 4x — 9 < 7 o r 3x - 10 > 2.
    50. Nut rit ion A sed en tary 15-year-old m ale sh o u ld consum e no m ore th an
    2200 Calories p er day. A m oderately active 15-year-old m ale should consum e
    betw een 2400 a n d 2800 Calories p er day. An active 15-year-old m ale should
    consum e betw een 2800 a n d 3200 Calories p e r day. M odel these ranges on a
    n u m b e r line. R epresent each range of calories using interval notation.

E

Po w er A lg eb r a.co m ^ 1 L e s s o n 3 - 6 Co m p o u n d In eq u al i t i es

---- ~ ..^......r...- .............= ~ ~

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