Algebra 1 Common Core Student Edition, Grade 8-9

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Got It? 2. W hat are th e solutions of - y < — 1? G raph an d check.

Solving inequalities using division is sim ilar to solving inequalities using m ultiplication.

If you divide each side of an inequality by a negative num ber, you n ee d to reverse the

direction of th e inequality symbol.

Key Concep t Division Property of Inequality

Let a, b, and c be real n u m b ers w ith c > 0. Ex a m p l e s

If a > b, th e n § > 6 > 3, so | > |.

If a < b, then § < c- 9 < 12, so | < y.

Let a, b, and c b e r e a l n u m b e r s w i t h c < 0.

If a > b, then § < 6 > 3, so ^ < J j.

If a < b, then f > §. 9 < 12, SO y g >

These properties are also tru e for inequalities using > a n d <.

k ...J

Dividing by a Positive Num ber

Think
What types of
solutions make sense
for this situation?
O nly w h o le -n u m b e r
solutions make sense
because you cannot w alk
p a rt o f a dog.

Par t - Ti m e Jo b You walk dogs in your neighborhood after school. You earn $4.50 per

dog. How many dogs do you need to walk to earn at least $75?

o i. Rel at e co st p e r , ^ t i m e s n u m b e r. c , is at least t l. a m o u n t. ,

dog of dogs wanted

Def ine Let d = th e n u m b e r of dogs.

W rit e 4.50 • d 75

4.50d > 75

4.50d.

4.50 =

75

4.50

d> 16|

Divide each side by 4.50.

Simplify.

However, since d represents th e n u m b e r of dogs, it m u st b e a positive integer. So you

m u st walk at least 17 dogs to ea rn at least $75.

Got It? 3. a. A stu d en t club plans to b uy food for a soup kitchen. A case of vegetables

costs $10.68. The club can sp en d at m ost $50 for this project. W hat are the

possible n u m b ers of cases th e club can buy?

b. Reasoning In Problem 3, why do you ro u n d to th e greater

w hole n um ber?

180 Ch ap t er 3 So lvin g In eq u alit ies