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).
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17. Example 5 : Solve the inequality and graph the solution set.
18. Example 6 : Solve the inequality and graph the solution set.
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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.
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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
40. But this is what is called a "strict" inequality. That is, it isn't an "or equals to" inequality; it's only " y greater than". 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 " y greater than" inequality, you want to shade above the line, so the solution looks like this:
![[object Object],[object Object],[object Object],[object Object]](https://image.slidesharecdn.com/linear-inequality-1234687288485258-3/85/Linear-Inequality-slayerix-1-320.jpg)
