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Question 74717: Graph the following inequalities.
4x + y "this symbol > with one line under it" 4
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 
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Let's begin by just making this expression and equation:
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Now graph this equation. Because the variables x and y have an understood exponent 1 you
can recognize this as a first degree linear equation. The graph is a straight line.
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You can easily graph the equation by first letting x equal zero. When you do, the equation
reduces to y = 4. So (0, 4) is on point on the graph. Next, let y = 0. When you do the equation
reduces to 4x = 4 and dividing both sides of that equation by 4 you get x = 1. So the point
(1, 0) is also on the graph. If you want more points, just assign other values to x and
solve the original equation for y. This will give you more points to confirm that you
have the correct line.
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After plotting these points, take a straight edge and run a line through them. This is the
graph of the equation 4x + y = 4.
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What does that mean? The graph represents the x,y points where 4x + y = 4. But the original
problem not only said that 4x + y = 4. It said that 4x + y is greater than 4. That means
that any x,y points that are above that graph will make 4x + y greater than 4. You can represent
that by shading the area above the line. The (x,y) points in that shaded area will make
4x + y greater than 4.
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So the answer is that any (x,y) point on the graph or in the shaded area above the graph
satisfy the inequality .
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Hope this helps you to understand problems of this type. You can treat them like equations,
with the exception that if you multiply or divide both sides of the inequality by a NEGATIVE
number, you must flip the inequality sign to point in the opposite direction. We did not
have to do that for this problem.
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