Linear Inequalities in Two Variables
Key Questions

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]}

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)# .
Questions
Linear Inequalities and Absolute Value

Inequality Expressions

Inequalities with Addition and Subtraction

Inequalities with Multiplication and Division

MultiStep Inequalities

Compound Inequalities

Applications with Inequalities

Absolute Value

Absolute Value Equations

Graphs of Absolute Value Equations

Absolute Value Inequalities

Linear Inequalities in Two Variables

Theoretical and Experimental Probability