Question 82620
Solve for y in {{{x-2y<=4}}}

{{{-2y<=4-x}}} Subtract x from both sides

{{{y>=(1/2)x-2}}} Divide both sides by -2


So the graph will have the equations {{{x=1}}}(which will be a dashed line) and {{{y=(1/2)x-2}}} (just replace the inequality signs with an equal sign)


{{{ graph( 300, 200, -6, 5, -10, 10, (1/2)x-2, 10000(x-1)) }}}


Now pick a test point (0,0) and evaluate it for {{{y>=(1/2)x-2}}}

{{{0>=(1/2)(0)-2}}}

{{{0>=-2}}} true. So shade the region containing (0,0). This is the region above the line

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Now pick a test point (0,0) and evaluate it for {{{x>1}}} (remember the x=1 line should be a dashed line)

{{{0>1}}}

{{{0>=-2}}} false. So shade the region that doesn't contain (0,0). This is the region to the right of the line.

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So the solution set will lie in the region that is created by the other two regions overlapping each other.


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