Download MR12 Lsn 3 How do we solve first degree equations and inequalities

Aim: How do we solve first degree
equations and inequalities?
 Do Now: Solve and Check
Solve for x:
1. (2x + 1) +( 4 – 3x) = 10
2. 2(x – 3) + 3(x + 4) = x + 14
3. 4x(x + 2) – x(3 + 4x) = 2x + 18
Solve and graph:
1)
4x  20
4x  20
4 4
x 5
0
2)
x
 2
3
x
(3)  2(3)
3
x  6
5
-6
0
6
Solve and graph
3x  6
3x  6
3  3
x  2
reverse
x  2
-2

2  3x  11
 3x  9
3x  9
x  3
-3

Solve and graph the inequalities.
3)
3x  18
3x  18
3
3
x  6
-6
0
m
 6
2
m
(2)
 6(2)
2
4)
m  12
-12
0
Solve and graph.
5) 3(x  4)  9
3x 12  9
12 12
3x  21
3x  21
3
3
x 7
0
7
6) 4x  3  2x 11
2x
 2x
6x  3 11
3  3
6x 14
6 6
7
x
3
1
2
0
3
Interval Notation
Interval
Notation
Inequality
Notation
[a, b]
a x b
a
b
x
Closed
[a, b)
a x<b
a
b
x
Half-open
(a, b]
a<x b
a
b
x
Half-open
(a, b)
a<x<b
a
b
x
Open
Line Graph
Type
1-3-5-1
Interval Notation
Interval
Notation
[b , )
( b,  )
( –, a]
(( –,, a)
Inequality
Notation
x b
x> b
x a
x< a
Line Graph
Type
b
x
b
x
Closed
Open
a
x

a
x
Closed
Open
1-3-5-2
Inequality Properties
For a, b, and c any real numbers:
1. If a < b and b < c, then a < c.
Transitive Property
2. If a < b, then a + c < b + c.
Addition Property
3. If a < b, then a – c < b – c.
Subtraction Property


5. If a < b and c is negative, then ca > cb. 
Multiplication Property
(Note difference between
4 and 5.)



Division Property
(Note difference between
6 and 7.)
4. If a < b and c is positive, then ca < cb.
a b
6. If a < b and c is positive, then c < .
c
a b
7. If a < b and c is negative, then c > c .
1-3-6