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You can put this solution on YOUR website!
Here's one way you can think about these problems.
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\n" ); document.write( "Let's begin by talking our way through:
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\n" ); document.write( "\n" ); document.write( "Let's start by presuming that the > sign is an equal sign and the equation actually is
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\n" ); document.write( "What does the graph of this equation look like? It is a horizontal line through the point
\n" ); document.write( "-2 on the y-axis. Does this make sense? What it says is that no matter what value you
\n" ); document.write( "select for x, the value of y will be -2.
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\n" ); document.write( "The reality is that the equal sign was only put in to help us picture what is going on
\n" ); document.write( "with the graph. Now we can put the > back into the equation. Now we can tell that the
\n" ); document.write( "values of y must be greater than -2. This means that y is allowed to be any value
\n" ); document.write( "above the line that is the graph. You can shade that entire region, but only the region
\n" ); document.write( "that is ABOVE the line. y can be any value in the shaded region. However, y cannot have
\n" ); document.write( "the value -2 because y is only allowed to be GREATER than -2. Therefore, y can NOT be
\n" ); document.write( "on the line.
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\n" ); document.write( "The next problem says that:
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\n" ); document.write( "Like we did before, let's temporarily replace the > sign with an equal sign. This changes
\n" ); document.write( "the equation to:
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\n" ); document.write( "This is in the slope-intercept form. Maybe you can picture the graph. It crosses the
\n" ); document.write( "y-axis at -2 and it slopes up and to the right at a rate of +2. That means for every 1 unit
\n" ); document.write( "you move horizontally to the right you go vertically up 2 units. You know that (0,-2) which
\n" ); document.write( "is the y-axis intercept is on the graph. You can easily find another point on the graph
\n" ); document.write( "by setting y = 0 in the line equation and then solving the equation for the corresponding
\n" ); document.write( "value of x:
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\n" ); document.write( "When you solve this you find that x = 2 is the answer. Therefore, you know that (2,0) is a
\n" ); document.write( "second point on the graph. With the two points (0,-2) and (2,0) plotted you can draw a line
\n" ); document.write( "through them and you will have the graph of
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\n" ); document.write( "At this point you should replace the = sign with the > sign to get back to the original
\n" ); document.write( "problem. This form tells you that y can only have values ABOVE the graph because y
\n" ); document.write( "must be greater than the values in the line. Shade the entire region above the line.
\n" ); document.write( "The shaded region is where values of y can be.\r
\n" ); document.write( "\n" ); document.write( "Finally, a little more complex (the last problem):
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\n" ); document.write( "We can solve this for to make it easier for us to find the region where y is allowed to
\n" ); document.write( "exist just as we did before. We want to solve for +y. So let's multiply both sides of
\n" ); document.write( "the equation by -1. However, here's an important rule: whenever you multiply or divide both
\n" ); document.write( "sides of an inequality by a negative number, you must afterward reverse the direction of
\n" ); document.write( "the inequality.
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\n" ); document.write( "Do the multiplication by -1 to get:
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\n" ); document.write( "But don't forget that you have to reverse the direction of the inequality sign too. When
\n" ); document.write( "you do the inequality is now:
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\n" ); document.write( "Now you can replace the inequality sign with an equal sign and solve the equation for y
\n" ); document.write( "just as you have always done. Begin by adding 4x to both sides to get:
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\n" ); document.write( "Divide both sides by 6 to solve for y and get:
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\n" ); document.write( "which becomes:
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\n" ); document.write( "Graph this equation as you did previously. The slope is (2/3) and the y-axis intercept
\n" ); document.write( "is -2.
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\n" ); document.write( "Now replace the = sign with the inequality sign pointing to the right so that the inequality
\n" ); document.write( "is now:
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\n" ); document.write( "Again, shade the entire region ABOVE the graph of the right side of the equation.
\n" ); document.write( "That represents the place where y is allowed. y can NOT be on or below the graphed line.
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\n" ); document.write( "After a little more practice you'll get familiar with this method and you can do things
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\n" ); document.write( "Hope this helps you with understanding the basic principles of doing problems such as
\n" ); document.write( "these inequalities.\r
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