Question 42763
{{{-4 <= 2*abs(u+3)- 8 }}}
add 8 to both sides
{{{4 <= 2*abs(u+3)}}}
divide both sides by 2
{{{2 <= abs(u+3)}}}
I can see that {{{u >= -1}}} and {{{u <= -5}}}
This problem can only be understood by plotting it.
plot {{{y <= abs(u+3)}}} by plotting
{{{y <= u + 3}}} and {{{y <= -u - 3}}}
{{{ graph( 300, 300, -10, 10, -10, 10, x+3, -x-3) }}}
The plot goes up and to the right with slope = +1, bounces off the u-axis
at (-3,0), then goes up and to the left with slope = -1, but 
everything below the horizontal line y = 2 must be excluded because
{{{2 <= abs(u+3)}}}. In summary, u can have ANY value except those
between u = -1 and u = -5. 
Note that, even though (-3,0) is not a valid point, u = -3 is
the axis of symmetry for the solution.
You can test this
Let u = +10
then y will be 13
If -3 is the axis of symmetry, y should have the same value on the
other side of u = -3
10 - (-3) = 13
-u - (-3) = 13
-u = 16
u = -16
{{{y <= abs(u+3)}}}
{{{+10 <= abs(10 + 3)}}}
{{{+10 <= abs(13)}}}
{{{+10 <= abs(-16 + 3)}}}
{{{+10 <= abs(-13)}}}
The right side shows that u = -3 is an axis of symmetry