Algebra 1 Common Core Student Edition, Grade 8-9

Go t It? 3. What is the graph of each inequality?

a. x< -5 b. y<2

Think
Whi ch i n eq u al i t y
symb o l shoul d
you use?
Yo u m u s t r e a d t h e
problem statement
caref ul ly. Here " $420
or less" means that the
so l u t i o n i ncl u d es, b ut
cannot exceed, $420,
so u se <.

When a linear inequality is solved for y, the direction of the inequality symbol

determines which side of the boundary line to shade. If the symbol is < or <, shade

below the boundary line. If the symbol is > or >, shade above it.

Sometimes you must first solve an inequality for y before using the method described

above to determine where to shade.

Rew r i t i n g t o Gr ap h an I n eq u al i t y

Interior Design An interior decorator is going to remodel a kitchen. The wall above

the stove and the counter is going to be redone as shown. The owners can spend $420

or less. Write a linear inequality and graph the solutions. What are three possible

prices for the wallpaper and tiles?

Let x = the cost per square foot of the paper.

Let y = the cost per square foot of the tiles.

Write an inequality and solve it fory.

24x + 12y < 420 To t al co st i s $420 or less. _

12y < -24x + 420 Su b t r ac t 2 4 * f r o m e ac h si d e. ^

y:£-2x + 35 Divide each side by 12. Q

_OJ

Graph y < - 2x + 35. The inequality symbol is < so the boundary line i=

is solid and you shade below it. The graph only makes sense in the first

quadrant. Three possible prices per square foot for wallpaper and tile are

$5 and $25, $5 and $15, and $10 and $10.

35

30

25

20

15

10

5

0

05 15 25

Pap er Co st , x ($)

^ Got It?4. For a party, you can spend no more than $12 on nuts. Peanuts

cost $2/lb. Cashews cost $4/lb. What are three possible combinations of

peanuts and cashews you can buy?

Pap er and

Ti l e Co st s

396 Chapter 5 Sy st e m s o f Eq u a t i o n s a n d I n e q u a l i t i e s