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WARM UPS 1/15
#1 Solve and graph the compound inequality –5 ≤ x – 1 ≤ 2
#2 Put the answer to #1 in set-builder notation.
#3 Solve and graph the inequality 5(x+2) > 25
Quiz
Grade Homework 5.3 & 5.4
CHAPTER 5.5Solving Absolute Value Inequalities
Case 1• Remove the absolute
value symbols.• Keep everything else the
same!
Case 2• Remove the absolute
value symbols.• Flip the inequality symbol.• Change the sign (positive
or negative) of the answer.
SOLVING ABSOLUTE VALUE INEQUALITIES
FIRST: Make two cases, and solve each individually…
SECOND: Graph both solutions on the same number line.
x – 3 < 12 x – 3 > -12
Case 1 Case 2
EXAMPLE #1X – 3 < 12
X + 4 < 6 X + 4 > -6
Case 1 Case 2
EXAMPLE #2X + 4 < 6
Case 1 Case 2
EXAMPLE #3X + 6 < -8
EXAMPLE #3X + 6 < -8
Since x + 6 can not be a negative, x + 6 cannot be less than -8
No Solution!
EXAMPLE #4RAINFALL
The average annual rainfall in California for the last 100 years is
23 inches. However, the annual rainfall can diff er by 10 inches
from the 100 year average. What is the range of annual rainfall for
California?
Case 1 Case 2
EXAMPLE #4RAINFALL
X – 23 < 10 X – 23 > -10
Case 1 Case 2
EXAMPLE #53X – 3 > 9
Case 1 Case 2
EXAMPLE #62X + 7 > -11
EXAMPLE #62X + 7 > -11
Since 2x + 7 is alwaysgreater than or equal to
0, the solution set is {x x is a real number}
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Activity…
HOMEWORKChapter 5.5
Problems 8-20, 43, 47
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