Ways to improve
•	Come to office hour, Wednesdays 10 - 11 after class.
•	Read sections, do examples and odd-numbered problems.
•	Go to math lab in room S-511 for free tutoring.
•	Attend class on time and ask questions.
•	Don't give up!

Graphing the solution set of a linear inequality.
≤,≥,<,>
3<4
4≤4
-1≥-4
-1>-2

-1<x

Solve for x and graph the solution.
− 7x + 4 > 3x + 44
+7x        = +7x

     4 > 10x + 44
  -44 =        - 44

-40 > 10x
10  =  10

-4 > x

− 7x + 4 > 3x + 44
-3x        = -3x

-10x + 4 > 44
        - 4  =  -4

-10x > 40
-10   = -10
x > -4

x > -4 > x
x > x (CONTRADICTION!)

To get the right answer we need to flip the inequality relation from < to >.
x < -4

Which gives us the correct answer.

•	Inequalities are similar to previous problems.
•	But dividing or multiplying by negatives changes the direction of the inequality. That is, < goes to >, < goes to >, ≤ to ≥ and ≥ to ≤.
•	Circles or dashed lines indicate that the points there are NOT included. This is necessary when we have a strict inequality (<, >).
•	When graphing an inequality in two variables, a dashed line represents strict inequalities.
•	We shade in all solutions to the inequality.
•	See sections 2.8, 2.9, 3.7 for more informaton.