Linear Inequalities in Two Variables
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Key Questions

The best way (when possible!) is to express the inequality bringing all the terms involing a variable on the left, and all the terms involving the other variable on the right. In the end, you'll have an inequality of the form
#y\le f(x)# (or#y\ge f(x)# ), and this is easy to graph, because if you can draw the graph of#f(x)# , then you'll have that#y\le f(x)# represents all the area under the function#f# , and#y\ge f(x)# , of course, the area over the function.For example, consider the inequality
#yx^2<y+3x#
In this form, it would be very hard to say which points satisfy the inequality, but with some manipulations we obtain
#yx^2+y<3x#
#y(x^2+1)<3x#
#y<\frac{3x}{x^2+1}# Now, the graph of
#\frac{3x}{x^2+1}# is easy to draw, and the inequality is solved considering all the area below the graph, as showed:graph{y<3x/{x^2+1} [10, 10, 5, 5]}
Note that if you have
#y<f(x)# the graph of the function#f# is not included, since it represents the points for which#y=f(x)# . 
The solution set of a single linear inequality is always a halfplane, so there are infinitely many solutions.
I hope that this was helpful.

Answer:
The direction of the inequality will tell you this information.
Explanation:
Example:
#y >= 2x+3# You would draw the line
#y = 2x+3# and shade above the line, since#y# is also greater than# 2x+3# .graph{y>=2x+3 [10, 10, 5, 5]}
Example:
#y < 1/2x2# You would draw the line
#y=1/2x2# as a dashed line, then shade below the line since#y# is less than#1/2x2# .graph{y<1/2x2 [10, 10, 5, 5]}

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Questions
Linear Inequalities and Absolute Value

1Inequality Expressions

2Inequalities with Addition and Subtraction

3Inequalities with Multiplication and Division

4MultiStep Inequalities

5Compound Inequalities

6Applications with Inequalities

7Absolute Value

8Absolute Value Equations

9Graphs of Absolute Value Equations

10Absolute Value Inequalities

11Linear Inequalities in Two Variables

12Theoretical and Experimental Probability