Download 2.5 Algebraic Proof Write a step-by

2.5 Algebraic Proof
Write a step-by-step solution of the linear equation by
placing the given equations in the correct order.
3(x-4) + 5 = 17
3x - 12 + 5 = 17
3x - 7 = 17
3x = 24
x=8
2-5 Reasoning with Properties from Algebra
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
Properties of Congruence:
Reflexive:
EF
EF,
A
A
Symmetric: If 1
2, then 2
Transitive: If AB
CD and CD
1
EF, then AB
EF
Example.
1.
3x + 12 = 8x - 18
12 = 5x - 18
30 = 5x
6 =x
2. C = 5 (F - 32)
9
Find F at 24 C
Solve for F.
Solve the equation.
Show all your steps and write the justification for each step.
4(x - 3) = -20
Write a justification for each step.
7x - 3
H
2x + 6
HJ = HI + IJ
7x - 3 = (2x + 6) + (3x - 3)
7x - 3 = 5x + 3
7x = 5x + 6
2x = 6
x = 3
I
3x - 3
J