Prvoving using Axioms of Real Numbers?

Question

Hi all. I've been out of school for a few years so I'm a bit rusty in my math skills. :-) I have this assignment due tomorrow, which I did but I just wanna make sure that I have it right. The assignment is to prove that if (x+4)/3 = 4 then x=8 (using the axioms/theorems of Real Numbers)

What I did first was to use the Multiplication Property of Equality so I multiplied the whole equation (both sides) by 3/1

Does anyone know the next steps? I know that the equation is pretty easy to solve but its just these steps that my professor wants us to know.

Help? Would appreciate it!

swd · Accepted Answer

If you want a step by step solution
(x+4) /3 = 4
1/3 * (x+ 4) = 4.........definition of division
3* [ 1/3 * (x+ 4) ] = 3 * 4.........multiplication property of =
3* [ 1/3 * (x+ 4) ] = 12.......simplification
[3* (1/3)] (x+4) = 12........associative axiom of *
(1)(x+4) = 12..........axiom of * inverse
x+4  = 12.... identity axiom of *
[x + 4] + (-4) = 12 + (-4) .... + property of =
[x + 4] + (-4) = 8.......simplification.
x + [4 + (-4)] = 8....associative axiom of +
x + 0 = 8.........axiom of additive inverse
x = 8...........identity axiom of +

This solution is long winded, but I understood from your question that you wanted to see how each axiom of the real number system is being used.

dutch_prof · Answer

After multiplying you find
... x + 4 = 12
Because 12 = 8 + 4, we may replace the right hand side:
... x + 4 = 8 + 4

Now use the Addition Property or Equality (also known as Cancellation Law) to remove the "+ 4".

... x = 8.

Sophist · Answer

The next one is property of equality and the property of addition/subtraction. (-4=-4), x+4-4=12-4 therefore x=8

Tom . · Answer

So far so good....
Now use the addition property to isolate the unknow x.

you should have    x+4 = 12

subtract 4 (or add -4) to each side   x = 8

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Prvoving using Axioms of Real Numbers?

4 Answers