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0.3 Inequalities
Solutions to inequalities are usually a SET of values, not just one solution or a finite number of solutions.
Usually, solving an inequality is just like solving an equation, differing only by occasionally switching the
inequality sign.
1
 x6
3
x  18
EXCEPTION: When the variable is in a denominator (because you don’t know if the variable is positive or
negative, therefore you don’t know what to do with > or < sign)
3
6
x
Theorem: The sign of a product depends on the signs of its factors.
AB > 0 iff (A > 0 and B > 0) or (A < 0 and B < 0)
AB < 0 iff (A > 0 and B < 0) or (A < 0 and B > 0)
Theorem: The sign of a product depends on its number of negative factors.
Ex) (-2)(-1)(2)(-6)
Ex)
(3)(2)(8)
(7)(4)
Ex) Solve by factoring
x2 < x
We can also TEST to see where the function is + or – because we know a polynomial changes signs at its
zeros.
x(x – 1) < 0 changes signs at ____________________
1. Test a point between  and 0
2. Test a point between 0 and 1
3. Test a point between 1 and 
Where is x(x – 1) < 0?
Inequalities and Absolute Value
 means “distance” (you can write d instead!)
| x  c |  and x  c   describe how close or far away x is to c.
A 
iff
A   and A   (that means the same thing as   A   !)
Ex) x 2  4  12
A 
iff
A   or A  
Ex) |2x – 5|>3
Ex)
1
1

x2 6 x
*NEVER cross multiply when you have an x in the denominator!
* Check your answer with a graphing calculator!
Homework: pg.34-35: 1a-d, 19, 23, 25, 31, 35, 41, 49, 53, 55, 59