Question 1046901
I really cannot follow your listing:
<pre>
1) a            1) given equation
2) 2x=2(5x+8)   2)b
3) c            3)distributive property of equality
4) 0=8x+16      4)d
5)  e           5)subtraction property of equality
6) -2=x         6)f
7)   g          7)symmetric property

</pre>

Your equation starts as  {{{2x=2(5x+8)}}}, and maybe you want to solve for x.  More than one way to do.


DISTRIBUTIVE PROP.   {{{2x=10x+16}}}


Be careful about "Subtraction Property of Equality", because none is.


Try ADDITIVE INVERSE, and ADDITION PROPERTY OF EQUALITY.
{{{2x+(-10x)=10x+16+(-10x)}}}
which basically means the same as
{{{2x-10x=10x+16-10x}}}
{{{-8x=16}}}


Next you need MULTIPLICATION PROPERTY OF EQUALITY.
{{{-8x(-1/8)=16(-1/8)}}}
{{{x=-2}}}
DONE.