Question 39207
{{{ abs(x - (1/2)) >= 2/3 }}} means we have 2 possibilities since the |.| part is like a V-shape, ie 2 straight lines. Mathematically we have to solve:


{{{ (x - (1/2)) >= 2/3 }}} and {{{ -(x - (1/2)) >= 2/3 }}}


First: {{{ (x - (1/2)) >= 2/3 }}} 
{{{ (x - (3/6)) >= 4/6 }}}
{{{ x >= 4/6 + 3/6 }}}
{{{ x >= 7/6 }}}


and now: {{{ -(x - (1/2)) >= 2/3 }}}
{{{ -x + (1/2) >= 2/3 }}}
{{{ -x + (3/6) >= 4/6 }}}
{{{ -x >= 4/6 - 3/6 }}}
{{{ -x >= 1/6 }}}
{{{ x <= -1/6 }}}


So, the value of x needs to be "less than or equal to" (-1/6) OR "greater than or equal to" (7/6)


Graphically, we can show this as {{{ graph(300,300,-2,3,-2,3,abs(x - (1/2)), (2/3)) }}}, where i have plotted both {{{ y = abs(x - (1/2)) }}} and {{{ y = 2/3 }}}. Where they cross each other are the 2 answers i calculated


jon.