Question 33565
y = |2x-2| means 2 straight lines: 2x-2 and -(2x-2). They form a V-shaped graph, as shown:


{{{ graph(300,300, -4, 6, -2, 10, abs(2x-2)) }}}


The question is asking "for what values of x is this graph less than or equal to y=2. Lets look at both these graphs:


{{{ graph(300,300, -4, 6, -2, 10, abs(2x-2), 2) }}}


Looking at the graph, the V-shape is less than or equal to the y=2 horizontal line between x=0 and x=2. These are the answers. Lets now try to get these 2 answers through algebra:


{{{ 2x-2 <= 2 }}}
{{{ 2x <= 4 }}}
{{{ x <= 4/2 }}}
{{{ x <= 2 }}}


and {{{ -(2x-2) <= 2 }}}
{{{ 2x-2 >= -2 }}} note the < has changed to a >
{{{ 2x >= 0 }}}
{{{ x >= 0 }}}


So, {{{ x >= 0 }}} and {{{ x <= 2 }}} 
or {{{ 0 <= x <= 2 }}} which matches the findings from the graph


jon.