Algebra 1 Common Core Student Edition, Grade 8-9

45. Rental Rat es The s tu d en t council w ants to re n t a ballroom for th e ju n io r prom.
    The ballroom 's rental rate is $1500 for 3 h a n d $125 for each additional h alf hour.
    Suppose th e s tu d e n t council raises $2125. W hat is th e m axim um n u m b e r of h ours
    for w hich they can rent the ballroom?


46. Writing Suppose a friend is having difficulty solving 3.75(q — 5) > 4 {q + 3).
    Explain how to solve th e inequality, show ing all th e n ecessary steps a n d identifying
    th e properties you w ould use.


47. Biology The average n o rm al body tem p eratu re for h u m a n s is 98.6°F. An abnorm al
    increase in b ody tem p eratu re is classified as h ypertherm ia, or fever. W hich
    inequality represents th e body tem p eratu re in degrees Celsius of a p erso n w ith
    hyperthermia? [Hint: To convert from degrees Celsius C to degrees F ahrenheit F,
    use th e form ula F = | c + 32.)

CA>|c+32>98.6 C 3 D |c+32<98.6 C O | c + 32 < 98.6 C O §C + 32 > 98.6

48. Open-Ended Write two different inequalities th a t you can solve by subtracting 3
    from each side an d th e n dividing each side by - 5. Solve each inequality.


49. a. Solve 6v + 5 £ 9v - 7 by gathering th e variable term s o n th e left side an d the
    co n stan t term s on th e right side of th e inequality.
    b. Solve 6v + 5 ^ 9v — 7 by gathering th e co n stan t term s o n th e left side a n d th e
    variable term s on the right side of th e inequality.
    c. C om pare th e results of p arts (a) an d (b).
    d. W hich m eth o d do you prefer? Explain.

@ 50. M ent al M at h D eterm ine w h e th e r each inequality is alw ays true o r never true.
a. 5s + 7 > 7 + 5s b. 4t+6>4t-3 c. 5(m + 2) < 5m - 4
51. Co m m i ssi o n A sales associate in a shoe store ea rn s $325 p er week, plus a
com m ission eq u al to 4% of h e r sales. This w eek h e r goal is to ea rn at least $475. At
least how m any dollars’ w orth of shoes m u st she sell in o rder to reach h er goal?

52. A s tu d en t uses th e table below to help solve 7y + 2 < 6(4 -y).

0.5

1.5

7(0.5) + 2 = 5.5 True 6(4 - 0.5) = 21

7(1) + 2 = 9

7(1.5) + 2 = 12.5

7(2) + 2 = 16

True 6 ( 4 - 1 ) = 18

True 6 ( 4 - 1. 5 ) = 15

False 6(4 - 2) = 12

a. Reasoning Based on th e table, w ould you expect th e solution of

7y + 2 < 6(4 - y) to be of th e form y < c or y > c, w here c is a real

n um ber? Explain.

b. Estimate Based o n th e table, estim ate th e value of c.

c. Solve th e inequality. C om pare th e actual solution to your estim ated solution.

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PowerAlgebra.com ^ I Lesson 3-4 Solving M ulti-Step Inequalities

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