Algebra 1 Common Core Student Edition, Grade 8-9

Why can you write an
and in e q u a lity w ith o u t
the word and!
The com pound in e q ua lity
-2 <n and n < 6
means n is greater than
-2 and n is less than 6.
This means n is between

• 2 and 6. You w rite this
  as - 2 < n < 6.

How do you know
to join the tw o
inequalities w ith and!
The com pound in e q u a lity
-3 s m -4 < —1
means th a t the quantity
m — 4 is between -3
and -1 , including -3.
So use th e w o r d and.

Writing a Compound Inequality

What compound inequality represents the phrase? Graph the solutions.

0 all real numbers that are greater

than - 2 and less than 6

n > — 2 and n < 6

-2 <n and n < 6

—2 < f t < 6

0 all real numbers that are less than 0 or

greater than or equal to 5

t < 0 or t > 5

ffl h + -0-*~

-1 1

"I I I I 1— © -

• 2 - 1 0 1 2 3 4 5 6

^ G o t It? 1. For parts (a) an d (b) below, w rite a co m p o u n d inequality th a t represents

each phrase. G raph th e solutions.

a. all real n u m b ers th a t are greater th a n or eq u al to —4 a n d less th a n 6

b. all real n u m b ers th a t are less th a n or equal to or greater th a n 6

| c. Reasoning W hat is th e difference betw een “x is b etw een - 5 an d 7" and

"xis b etw een —5 a n d 7, inclusive”?

A solution of a c o m p o u n d inequality involving and is any n u m b e r th at m akes both

inequalities true. O ne way you can solve a co m p o u n d inequality is by separating it into

two inequalities.

Solving a Compound Inequality Involving And

What are the solutions o f - 3 < m - 4 < —1? Graph the solutions.

—3 < m — 4 < —1

, W rite th e com pound in e q u a lity as tw o

~m an m inequalities joined by the word and.

-3 + 4 < m - 4 + 4 and m - 4 + 4 < - l + 4 Add 4 to each side of each inequality.

1 < m and m< 3 Simplify.

1 < m < 3 W rite th e s olu tio n s as a single inequality.

-«— l----- 1 ------ 1 ----- 1 -----» A <D— I----1—

-3-2-1012345

v ^ G o t It? 2. W hat are the solutions of —2 < 3y — 4 < 14? G raph the solutions.

You can also solve a n inequality like — 3 ^ ra — 4 < — l b y w orking on all th ree parts of

th e inequality at th e sam e time. You w ork to isolate th e variable betw een th e inequality

symbols. This m e th o d is u sed in P roblem 3.

f | Lesson 3-6 Co m p o u n d In eq u al i t i es^201

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