Squiggly Line Method for Solving Polynomial
Inequalities
Solve the inequality: 
- Draw a number line.
- Mark the points where the inequality equals 0 or
is undefined
-- in numerical order. Use a closed circle for values that may be
used as solutions and an open circle for values that make the
expression
undefined.
________o______________o______________o|___________o_____
-3 -2
1 3
- Choose a point in one of the intervals, preferably the right or
left
end, and plug a number from that interval into the original equation to
see if the answer would be positive or negative. If the answer is
positive
start the squiggly line above the number line and if it is negative
start
it below.
I chose to plug in +4. The answer would be
positive,
so I start my squiggly line above the number line in the area where x
would be larger than 3, and draw it down to meet the
number
line at 3. I should also have closed circles
on 3, -2, and 1, and
an
open circle on -3.
_/
________o_____________o______________o___________o_/______
-3 -2
1
3
- The factor from which the zero came has a power that is either
even
or odd. If the power is even, the squiggly line should bounce off that
zero. If the power is odd, the squiggly line should go through that
zero.
/
____________ _____________ /
_______o/___________\o_________
___o/____________ \|o/______
__ / -3
-2\ / 1 3
/ \________ __/
/
/
- The interval for which this squiggly line is below the number
line
or on the number line (marked by a closed circle) is the answer to this
particular problem.
Answer: x < -3, -2 < x < 1, x
=
3
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