How do I display a way to prove an "equation" is an identity? ?

Question

I know that 2(4x + 14) = 8x + 28 is an "identity", but how do I determine this (that is, show my work)? Can someone show me how this is determined, and/or use another example? Thank you!

Answer 1

Yeah, just fix it so 8x + 28 = 8x + 28, and you call it a reflexitive identity, (just remember reflection).

Answer 2

If you can work on each side of the equation and get, eventually, to

x=x

Then you've demonstrated that the equation in question was an identity.

I'd start by multiplying each side by 1/2:

(4x + 14) = 4x + 14

Subtract 14:

4x = 4x

Divide by 4

x = x

Whee!

Answer 3

You can't prove anything without axioms.  The three most basic axioms are commutative, associative and distributive axioms.  You need to learn these.

2(4x + 14) = (2*4x + 2*14)  by distribution

2*4x +2*14 = (2*4)x + 2*14 by association

(2*4)x + (2*14) = 8x+28 by calculation

Answer 4

simplify the left and right hand sides of the equation to its simplest form, which would be like

showing x = x

or 1 = 1

and that's an identity

Answer 5

Just show both sides are identical. Use the distributive property on the left to get 8x + 28 = 8x+28

Answer 6

Just start with one side and show that after algebraic manipulation, it is equal to the right side...

2(4x + 14) distribute

= 8x + 28

8x+28 = 8x+28 (identitiy)