Download Section 2.1

ALGEBRA II. NOTES
SECTION 2.1 SOLVING INEQUALITIES IN ONE VARIABLE
In the last chapter, we worked with solving equations in 1 variable:
Ex.) 2x  3  17
What if we replace the equals sign with an inequality symbol? How is our solution
affected?
Ex.) 2x  3  17
Note: 1.) use an open circle when graphing inequalities containing < or >.
2.) use a closed circle when graphing inequalities containing  or  .
So to solve inequalities, we’re basically doing the same steps as the ones used in solving
equations with 1 exception:
Multiplying or dividing by a negative:
Ex.) 6x  12
A.) STEPS TO SOLVE INEQUALITIES:
1.) Simplify both sides.
2.) Add to or subtract from both sides.
3.) Multiply or divide each side by a nonzero #. (If multiplying or dividing by a
negative, switch the inequality.)
B.) Equivalent Inequalities – transformations that produce inequalities with the same
solution set.
Ex.) 2 x  14 and x  7
C.) PROPERTIES OF ORDER – Let a, b, and c be real #’s.
1.) Comparison Property – exactly 1 of the following statements is true:
a  b, a  b, a  b .
2.) Transitive Property – If a  b and b  c , then a  c .
3.) Addition Property – If a  b , then a  c  b  c .
4.) Multiplication Property –
a.) If a  b and c is positive, then ac  bc .
b.) If a  b and c is negative, then ac  bc .
Oral Exercises: pgs. 61–62 #5-17
Sample Problems: pgs. 62-63
12.) 3t  6t  12
18.) 4s  3(2  3s)  5(2  s)
22.)
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t  (2  3t )  5t  2(1  t )
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