Question 5208
One way to solve this is to first solve for y by adding +4x to each side:
2y - 4x < 8
2y - 4x + 4x < 4x + 8
2y < 4x+ 8


Next divide both sides by 2:

{{{(2y)/2 < (4x)/2 + 8/2}}}
{{{y < 2x + 4}}}

You can graph the equation y = 2x +4, by seeing that the y-intercept is 4, and the slope is 2 or {{{2/1 = (rise)/ (run)}}}.  The result of this equation is graphed below.


{{{ graph (300,300, -10, 10, -10, 10, 4x+4) }}}


Now, what the inequality {{{y < 2x + 4}}} calls for is to use a dotted line (since this does NOT include the line), and because the problem calls for y <, you shade below the line.  If it had been y> 2x + 4, then you would have shaded ABOVE the line.  One more detail, this rule about shading above (for y> ) and below the line (for Y < ) this rule only applies when y has a positive coefficient.  Unfortunately, I haven't learned to graph a shaded area in this website yet.  Maybe Ichudov will show us how to do this here.  Until then, you'll have to do this for yourself:  Graph this with a dotted line, and shade below the line.


I hope that is helpful and not confusing.


R^2 at SCC