4x 3 9 and 2 5x < 7 - university of alaska...

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,∞)