4x 3 9 and 2 5x < 7 - university of alaska...
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Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12,
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12,x < 3,
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3,
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
Graph x < 3
-2 -1 0 1 2 3 4
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
Graph x > −1
-2 -1 0 1 2 3 4
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
Graph the portion under both.
-2 -1 0 1 2 3 4
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the left endpoint?
( )
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the left endpoint? -1
(− 1, )
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the right endpoint?
(− 1, )
Multiple Inequalities
4x− 3 < 9, and 2− 5x < 7.4x < 12, and −5x < 5.x < 3, and x > −1.
-2 -1 0 1 2 3 4
What is the right endpoint? 3
(− 1, 3)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49,
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49,x < −7,
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7,
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
Graph x < −7
-10 -7.5 -5 -2.5 0 2.5 5 7.5
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
Graph x > 4
-10 -7.5 -5 -2.5 0 2.5 5 7.5
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
Graph the portion under either.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint?
( )
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint? There is none.
(−∞, )
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint?
(−∞, )
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint? -7
(−∞, − 7)
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint?
(−∞, − 7) ∪ ( )
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the left endpoint? 4
(−∞, − 7) ∪ (4, )
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint?
(−∞, − 7) ∪ (4, )
Multiple Inequalities
11− 7x > 60, and 3x− 11 < 1.−7x > 49, and 3x < 12.x < −7, and x > 4.
-10 -7.5 -5 -2.5 0 2.5 5 7.5
What is the right endpoint? There is none.
(−∞, − 7) ∪ (4,∞)