October 04, 2011
3(x-4) + 5 = 17
3x - 12 + 5 = 17
3x - 7 = 17
3x = 24
x=8
October 04, 2011
10y + 5 = 25
10y + 5 - 5 = 25 - 5
10y = 20
10y = 20
10 10
y=2
October 04, 2011
6x + 3 = 9(x - 1)
6x + 3 = 9x - 9
6x - 9x + 3 = 9x - 9x - 9
-3x + 3 = -9
-3x + 3 - 3 = -9 - 3
-3x = -12
-3x = -12
-3
-3
x=4
October 04, 2011
2-5
Reasoning with Properties from Algebra
*Activity
Properties of Equality
addition: you can add the same thing to both sides of the equ.
subtraction: you can subtract the same thing from both sides of the equ.
multiplication: you can multiply both sides of an equ. by the same number
division: you can divide both sides of an equ. by the same number.
reflexive: anything equals itself (a = a)
symmetric: you can switch all items with respect to the equal sign
(If a = b, then b = a)
transitive: if 2 items equal the same item, then the two items equal each
other (If a = b and b = c, then a = c)
substitution: an equivalent item may be substituted in for something
distributive: a(b + c) = ab + ac
October 04, 2011
Properties of Congruence:
Reflexive:
EF
EF,
Symmetric: If 1
Transitive: If AB
A
A
2, then 2
CD and CD
1
EF, then AB
EF
October 04, 2011
Example.
1.
3x + 12 = 8x - 18
12 = 5x - 18
30 = 5x
6 =x
October 04, 2011
2. C = 5 (F - 32)
9
Find F at 24 C
Solve for F.
October 04, 2011
5. The pitcher's mound is at
3. Find m 4.
m 1 + m 2 + m 3 = 180
m 1 + m 2 = 93
m 3 + m 4 = 180