Warm-Up

1
Warm-Up

• Evaluate each expression, given that x3 and
  y-2.
• a. 2x -9
• Answer
• 1) -3 2) 3 3) 15 4) -15
• b. y x
• Answer
• 1) -5 2) 1 3) -1 4) 5
• Solve.
• 3x 6 9
• Answer
• 1) x1, -5 2) x -1, 5 3) x 3, -15 4) x -3, 15

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6.4 Absolute Values and Inequalities

• Objective
• Learn how to solve absolute value inequalities.

3
Review

• Why is the absolute value of a number always
  greater than or equal to zero?
• Two or more inequalities connected by the words
  _______ or _________ are a compound inequality.

4

• Less Than when an absolute value is on the left
  and the inequality symbol is lt or , the compound
  sentence uses and.

Conjunction ax b lt c Means x is between
c -c lt ax b lt c
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Disjunction ax b gt c Means not
between! ax b lt -c or ax b gt c Greater
Than when an absolute value is on the left and
the inequality symbol is gt or , the compound
sentence uses or.
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(No Transcript)
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Solving absolute inequalities and graphing
x - 4 lt 3 (less than is between) Means -3 lt
x- 4 lt 3 (solve) Graph
4
4
4
1lt xlt 7
0 1 2 3 4 5 6 7 8 9
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Solving absolute inequalities and graphing

• s 3 12 (less than is between)
• Means -12 s 3 12 (solve)
• 3 3 3
• - 9 s 15
• Graph
• -9 -6 -3 0 3 6 9 12 15 18 21 24

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Check Your Progress

• Solve each absolute value inequalities then
  graph.
• A. y 4 lt 5
• B. z 3 2

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Solve and graph x 9 gt 13 (disjunction) Mean
s x 9 lt -13 or x 9 gt 13
-9
-9
-9
-9
x lt -22
x gt 4
Graph
-25 -20 -15 -10 -5 0 5 10
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Check Your Progress

• Solve each absolute value inequalities and graph.
  
• A. 3y 3 gt 9
• B. 2x 7 11

12

• Change the graph to an absolute value
  inequality
• 1. Write the inequality. (x is between)
• 2 lt x lt 8
• Find half way between 2 and 8
• Its 5 (this is the median)
• To find the median, add the two numbers and
  then divide by 2. 28 5

0 1 2 3 4 5 6 7 8 9 10
2
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3. Now rewrite the inequality and subtract 5
(the median) from each section. 2 - 5 lt x - 5 lt
8 - 5 Combine like terms or numbers and you
get -3 lt x - 5 lt 3 4. Write your absolute
inequality x - 5 lt 3
Notice The median is 3 units away from either
number.
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Write the inequality for this disjunction
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
7 8

• x lt -6 or x gt 4 (find the median)
• 2. x 1 lt - 5 x1 gt 5
• 3. x1gt5

1
1
1
1
(subtract -1 from both sides, so add 1)
(write x 1 inside the absolute brackets and 5
outside positive)
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Check Your Progress

• Write an absolute value inequality for the graph
  shown
• -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
  6 7 8

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
7 8
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Closing the lesson

• Summarize the major points of the lesson and
  answer the Essential Question How are absolute
  value inequalities like linear inequalities?

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Homework

• Textbook page 316 8-30 even, 31 36, 38 40