Algebra 1 Common Core Student Edition, Grade 8-9

Got It? 4, W h a t a re th e s o lu t io n s o f 12x + 4 1 > 5? G r a p h t h e s o lu tio n s.

Th?nk ffra
How else could you
write this inequality?
You could break the
compound inequality
into two parts:
w - 213 a - 5 and
w-213<5.

So l v i n g a n A b so l u t e V a l u e I n e q u a l i t y I n v o l v i n g < Q2 2 )

Manufacturing A c o m p a n y m a k e s b o x e s o f c r a c k e r s t h a t s h o u ld w e ig h 2 1 3 g. A

q u a l i t y - c o n t r o l in s p e c t o r r a n d o m l y s e le c ts b o x e s t o w e ig h. A n y b o x t h a t v a r ie s f r o m

t h e w e ig h t b y m o r e t h a n 5 g is s e n t b a c k. W h a t is t h e r a n g e o f a llo w a b le w e ig h t s f o r a

b o x o f c r a c k e r s?

difference between actual

Relate an(j jjg a i w eights is a t m o s t 5g

Define Let w = th e a c tu a l w e ig h t in g ra m s.

Write \w — 2131 < 5

\w-213| < 5

-5 ^w - 213 < 5 Write a compound inequality.

208 < w ^ 2 1 8 Add 213 to each expression.

T h e w e ig h t o f a b o x o f c r a c k e r s m u s t b e b e t w e e n 2 0 8 g a n d 2 1 8 g, in c lu s iv e.

Go t I t? 5. a. A f o o d m a n u f a c t u r e r m a k e s 3 2 - o z b o x e s o f p a s ta. N o t e v e r y b o x w e ig h s

e x a c tly 3 2 o z. T h e a llo w a b le d if f e r e n c e f r o m th e id e a l w e ig h t is a t m o s t

0 .0 5 o z. W r it e a n d s o lv e a n a b s o lu te v a lu e in e q u a l i t y t o f i n d th e r a n g e o f

allowable weights,

b. Reasoning I n P r o b le m 5, c o u ld y o u h a v e s o lv e d t h e i n e q u a l i t y

| w — 2 1 3 1 < 5 b y f ir s t a d d in g 2 1 3 t o e a c h s id e? E x p la in y o u r r e a s o n in g.

J Lesson Check

Do y o u k n o w H OW?

S o lv e a n d g r a p h e a c h e q u a t i o n o r i n e q u a l i t y.

1 .|x | = 5

2 .| n | — 3 = 4 @7.

3. \2t\ =6
   00
   4.|fc — 3 | < 5


4. |x + 2 | > 1

_. .. ______MATHEMATICAL

Do y o u UN DERSTAND? U g J PRACTICES

6. R e a s o n i n g H o w m a n y s o lu t io n s d o y o u e x p e c t t o g e t

when you solve an absolute value equation? Explain.

Writing Explain why the absolute value equation

|3x| +8 = 5 has no solution.

Compare and Contrast E x p la in t h e s im ila r it ie s

a n d d iffe r e n c e s i n s o lv in g th e e q u a t io n |jc — 11 = 2

with solving the inequalities |x - 11 < 2 and

|x — 11 > 2.

210 Chapter 3 Solving Inequalities