Question 730560
the absolute value function is always something like this:

f(X)=|g(x)| if you want to remove absolute sign and write a simple model of function instead it's as follow:

f(X)=|g(x)| is equal to two different function all the time:

1) for {{{X<0}}} >>>  {{{f(X)=-1*g(x)}}} and
2) for {{{X>0}}} >>>  {{{f(X)= 1*g(x)}}}

so in this case:
{{{f(X)=7}}} and {{{g(x)=6x-3}}}
 so,
1) for {{{X<0}}} >>>  {{{7=-1*(6x-3)}}}  >>> {{{7=-6x+3)}}} >>>{{{4=-6x)}}} >> {{{X=-2/3)}}} 

since you assumed that X should be negative at the first place {{{X<0}}} and you find {{{X=-2/3)}}} it is a valid answer, otherwise if it was not negative, it was not acceptable.

2) for {{{X>0}}} >>>  {{{f(X)= 1*g(x)}}} >>> {{{7=6x-3)}}} >>> {{{10=6x)}}} >>> {{{X=5/3)}}} again since it's a positive as we assumed for this case it is acceptable.

in conclusion the answers are : {{{-2/3}}} and {{{5/3}}}