Question 70283
Here's one way you can think about these problems.
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Let's begin by talking our way through:
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{{{y>(-2)}}}

Let's start by presuming that the > sign is an equal sign and the equation actually is
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{{{y = -2}}}
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What does the graph of this equation look like? It is a horizontal line through the point
-2 on the y-axis.  Does this make sense?  What it says is that no matter what value you
select for x, the value of y will be -2. 
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The reality is that the equal sign was only put in to help us picture what is going on
with the graph.  Now we can put the > back into the equation.  Now we can tell that the
values of y must be greater than -2.  This means that y is allowed to be any value 
above the line that is the graph.  You can shade that entire region, but only the region
that is ABOVE the line.  y can be any value in the shaded region.  However, y cannot have
the value -2 because y is only allowed to be GREATER than -2.  Therefore, y can  NOT be
on the line. 
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The next problem says that:
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{{{y>2x-2}}}
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Like we did before, let's temporarily replace the > sign with an equal sign.  This changes
the equation to:
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{{{y = 2x - 2}}}
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This is in the slope-intercept form.  Maybe you can picture the graph.  It crosses the
y-axis at -2 and it slopes up and to the right at a rate of +2.  That means for every 1 unit
you move horizontally to the right you go vertically up 2 units. You know that (0,-2) which
is the y-axis intercept is on the graph.  You can easily find another point on the graph
by setting y = 0 in the line equation and then solving the equation for the corresponding
value of x:
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{{{0 = 2x - 2}}}
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When you solve this you find that x = 2 is the answer.  Therefore, you know that (2,0) is a 
second point on the graph.  With the two points (0,-2) and (2,0) plotted you can draw a line 
through them and you will have the graph of {{{y = 2x - 2}}}
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At this point you should replace the = sign with the > sign to get back to the original 
problem.  This form tells you that y can only have values ABOVE the graph because y
must be greater than the values in the line. Shade the entire region above the line.
The shaded region is where values of y can be.

Finally, a little more complex (the last problem):
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{{{4x-6y<12}}}
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We can solve this for to make it easier for us to find the region where y is allowed to 
exist just as we did before. We want to solve for +y.  So let's multiply both sides of
the equation by -1.  However, here's an important rule: whenever you multiply or divide both
sides of an inequality by a negative number, you must afterward reverse the direction of
the inequality.
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{{{(-1)*(4x-6y)<(-1)*(12)}}}
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Do the multiplication by -1 to get:
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{{{-4x + 6y < -12}}}
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But don't forget that you have to reverse the direction of the inequality sign too.  When
you do the inequality is now:
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{{{-4x + 6y > -12}}}
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Now you can replace the inequality sign with an equal sign and solve the equation for y
just as you have always done.  Begin by adding 4x to both sides to get:
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{{{   +6y = 4x - 12}}}
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Divide both sides by 6 to solve for y and get:
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{{{y = (4/6)*x - 12/6}}}
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which becomes:
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{{{y = (2/3)*x - 2}}}
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Graph this equation as you did previously. The slope is (2/3) and the y-axis intercept
is -2.
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Now replace the = sign with the inequality sign pointing to the right so that the inequality
is now:
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{{{y > (2/3)*x - 2}}}
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Again, shade the entire region ABOVE the graph of the right side of the equation.
That represents the place where y is allowed.  y can NOT be on or below the graphed line.
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After a little more practice you'll get familiar with this method and you can do things
faster and without thinking about it.
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Hope this helps you with understanding the basic principles of doing problems such as
these inequalities.