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