geometry help; properties from algebra and proof?

Question

prove that if 2/3x= -8, then x=12.
given: 2-3x= -8.
prove: x=-12

statements:
a. 2/3x= -8
b. 2x= -24
c. x= -12

reasons:

a.
b.
c.

prove that if 5=2-1/2x, then x= -6.
given: 5=2- 1/2x
prove: x= -6

statements:
a. 5=2- 1/2x
b. 2- 1/2x=5
c. 2(2- 1/2x)=10
d. 4-x=10
e. -x=6
f. x= -6

reasons:

a.
b.
c.
d.
e.
f.

prove that if 2x-7-1/3x-2, then x=3.
given: 2x-7=1/3x-2
prove: x=3

statements:
a. 2x-7=1/3-2
b. 3(2x-7)=3(1/3x-2)
c. 6x-21=x-6
d. 5x-21= -6
e. 5x=15
f. x=3

reasons:

a.
b.
c.
d.
e.
f.


thanks so much.
<3; ms aungg.

Answer 1

you should ask one question at a time
get an answer and then see if you can do it yourself
if not then ask another one

1.

(2/3) x = -8 ........ given
2x = -24 ............ multiplication property of equality
x = -8 .................Division property of equality

Answer 2

given: 2/3x= -8.
prove: x=-12
statements:
a. 2/3x= -8
b. 2x= -24
c. x= -12
reasons:
a. Given
b. If equals are multiplied by equals the products are equal
c. If equals are divided by equals the quotients are equal

prove that if 5=2-1/2x, then x= -6.
given: 5=2- 1/2x
prove: x= -6
statements:
a. 5=2- 1/2x
b. 2- 1/2x=5
c. 2(2- 1/2x)=10
d. 4-x=10
e. -x=6
f. x= -6
reasons:
a. Given
b. Commutative law Addition
c. Multiplication Axiom
d.Distributive property
e.Subtraction Axiom
f.Multiplication Axiom

prove that if 2x-7-1/3x-2, then x=3.
given: 2x-7=1/3x-2
prove: x=3
statements:
a. 2x-7=1/3-2
b. 3(2x-7)=3(1/3x-2)
c. 6x-21=x-6
d. 5x-21= -6
e. 5x=15
f. x=3
reasons:
a. Given
b. Multiplication Axiom
c.Distributive Property
d.Subtraction Axiom
e. Addition Axiom
f. Division Axiom

Answer 3

They have given you much information. Usually, geometric proofs do not have so much data. Did you try any of these yourself?

I will do one of them as your guide.

We have:

geometry help; properties from algebra and proof?
prove that if 2/3x= -8, then x=12.
given: 2-3x= -8.
prove: x=-12

Statements:

a. 2/3x= -8
b. 2x= -24
c. x= -12

Reasons:

a.Given
b.Division Property of Equality
c.Solution of original equation

Look:

If you plug x = -12 into the orginal equation given, you'll get the same answer on BOTH sides of the equation. In other words, you create a BALANCE, which is the true definition of the word equation anyway.

Here's a good site for you:

http://www.themathlab.com/geometry/mathcourt/writeproofs.htm