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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