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2. Linear Inequalities Mathematics Presentation

12. Example 2 : Graph x < 2. Since we needed to indicate all values less than or equal to 2, the part of the number line that is to the left of 2 was darkened. Since there is an equal line under the < symbol, this means we do include the endpoint 2. We can notate that by using a closed hole (or you can use a boxed end).

17. Example 5 : Solve the inequality and graph the solution set.

18. Example 6 : Solve the inequality and graph the solution set.

20. Example 7 : Solve the inequality and graph the solution I multiplied by a -2 to take care of both the negative and the division by 2 in one step. In line 2, note that when I did show the step of multiplying both sides by a -2, I reversed my inequality sign.

22. Example 10 : Solve the inequality and graph the solution Even though we had a -2 on the right side in line 5, we were dividing both sides by a positive 2, so we did not change the inequality sign.

23. Example 11 : Solve the inequality and graph the solution

31. Solving linear inequalities

40. But this is what is called a &quot;strict&quot; inequality. That is, it isn't an &quot;or equals to&quot; inequality; it's only &quot; y greater than&quot;. When you had strict inequalities on the number line (such as x < 3), you'd denote this by using a parenthesis (instead of a square bracket) or an open [unfilled] dot (instead of a closed [filled] dot). In the case of these linear inequalities, the notation for a strict inequality is a dashed line. So the border of the solution region actually looks like this:

41. By using a dashed line, you still know where the border is, but you also know that it isn't included in the solution. Since this is a &quot; y greater than&quot; inequality, you want to shade above the line, so the solution looks like this: