Linear Inequality slayerix
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1) Solving linear inequalities involves using the same concepts as solving linear equations to isolate the variable, but inequalities have infinite solutions rather than a single solution. 2) Inequality signs (<, >, ≤, ≥) indicate whether values are less than, greater than, less than or equal to, or greater than or equal to another value. 3) Graphing linear inequalities on a number line or coordinate plane involves graphing the corresponding equality and then shading the appropriate side based on the inequality sign and whether it includes the endpoint or not.
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Linear Inequality slayerix
- 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
- 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: