You can put this solution on YOUR website!
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First solve this inequality for y.
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Use the same method as you would use in solving an equation ... (for the time being you
can sort of imagine that the > sign is an equal sign).
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Begin by adding x to both sides to remove the -x from the left side. When you do that the
inequality becomes:
.
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Now to solve for y you divide both sides by -2. This results in:
.
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At this point we have to take care of another inequality rule. This rule says that whenever
you divide or multiply by a negative number you also need to reverse the direction of
the inequality sign. We divided by negative 2, but we have not reversed the direction
of the inequality sign. So let's do that before we forget it. The inequality becomes:
.
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Do the algebra on the right side to get:
.
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That's the solution you need. Notice that if the "<" sign were replaced by an equal sign
you would have an equation in the slope-intercept form. The slope would be
and the y-intercept would be -2.
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If you graphed this equation
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The graph would look like:
.
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How do we interpret this? We know that the equation for this graph is:
.
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but when we add the inequality sign that we got, it tells us that y must be below this
graph (or less than the graphed line, if you prefer). So shade in everything below
this line. That shaded area is the region of all values of y that satisfy the inequality.
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Note that y cannot be on the line because the inequality sign says "less than". If the sign
was "less than or equal to" then y could be on the graphed line as well as below it.
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Hope this helps you to understand a little more about solving inequalities and graphing them
as well.
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