A)

INEQUALITIES:

alb,

a(b,

a>b,

a<b

B) TNTERVALS

ON

Trm

X-AXrS:

1) OPEN:

>Pb,

x(b, a(x<b.

Also written

as

(b;co), (-*;b),

(a;b)

GRAPHS b<x,

b>x, aSxSb.

resp.

2)

Closed:

Pa, x<b,

asx<b. Also

written

as

[a;co),

(-o;b],

[a;b]

o->

GRAPHS:

b<&

b>t

a<x<b,

resp.

3)

I{ALF-OPEN

OR

IIALF-CLOSED: (a;bl,

[a;b)

a<x<b, aSx<b, resp.

C)

SOLVING

LINEAR INEQUALITIES:

Note:

Rules

are the same

as for

equations

except for

one.

Multiplying

or

dividing

both

sides

by

a

negative

quantity

reverses

the

direction

of

the inequality.

Note:

You

can avoid

this complication

if

you get

a

positive

coefficient

for

the variable.

Examples:

2x-3>5-+2x>8-+x>4,

7-5x<2+5<5x+1<x

Note:

Be

careful

when solving inequalities

with

variable

denominators.

When multiplying

both

sides by a

variable

quantity,

you

must

consider

both

positive

&

negative

cases

for

the

quantifi

(i.e.,

when

solving

(x-1)/(2x+3)

>

0)

(will

solve

these

later)

BASIC

REYIEW

+-o

+.