Question 42764
Here's the scoop. When you see the absolute value signs,
do whatever's inside them as if they weren't there.
Then, whatever the sign of the result is, make it POSITIVE.
Also, abs(a + b) does not equal  abs(a) + abs(b)
You can see this by choosing a & b
abs(3 + (-5)) =?  abs(3) + abs(-5)
2 not equal to 8
{{{abs(ab) = abs(a)*abs(b)}}}
{{{abs(a/b) = abs(a)/abs(b)}}}
------------------------------
{{{abs(9x+8) = abs(-3x+9)}}}
I applied a little logic here. It's a dumbed-down 
approach, but it works.
x will be positive OR negative. It might be either one,
so I'll try both cases. I'll say x = +a OR x = -a.
I'll drop the absolute value sign and pick them up
later.
{{{9*a + 8 = -3*a + 9}}}
{{{12a = 1}}}
{{{a = 1/12}}}
and the other possibility,
{{{9*(-a)+ 8 = -3*(-a) + 9}}}
{{{-12a = 1}}}
{{{a = -1/12}}}
check the 1st case, a = 1/12
{{{abs(9x+8) = abs(-3x+9)}}}
{{{abs(9(1/12)+8) = abs(-3(1/12)+9)}}}
{{{abs((9/12)+8) = abs((-3/12)+9)}}}
{{{abs((9/12)+(8*12)/12) = abs((-3/12)+(9*12)/12)}}}
{{{abs(9/12 + 96/12) = abs(-3/12 + 108/12)}}}
{{{abs((9 + 96)/12) = abs((-3 + 108)/12)}}}
{{{abs(105/12)) = abs(-105/12)}}}
this is TRUE
Let's check the other possibility, a = -1/12
{{{abs(9(-1/12)+8) = abs(-3(-1/12)+9)}}}
{{{abs((9/12)+(8*12)/12) = abs((3/12)+(9*12)/12)}}}
{{{abs((9 + 96)/12) = abs((3 + 108)/12)}}}
{{{abs(105/12) = abs(111/12)}}}
NOT TRUE
So a = +1/12, and x = +1/12